The minmin coalition number in graphs

A set $S$ of vertices in a graph $G$ is a dominating set if every vertex of $V(G) \setminus S$ is adjacent to a vertex in $S$. A coalition in $G$ consists of two disjoint sets of vertices $X$ and $Y$ of $G$, neither of which is a dominating set but whose union $X \cup Y$ is a dominating set of $G$. Such sets $X$ and $Y$ form a coalition in $G$. A coalition partition, abbreviated $c$-partition, in $G$ is a partition $\mathcal{X} = \{X_1,\ldots,X_k\}$ of the vertex set $V(G)$ of $G$ such that for all $i \in [k]$, each set $X_i \in \mathcal{X}$ satisfies one of the following two conditions: (1) $X_i$ is a dominating set of $G$ with a single vertex, or (2) $X_i$ forms a coalition with some other set $X_j \in \mathcal{X}$. %The coalition number ${C}(G)$ is the maximum cardinality of a $c$-partition of $G$. Let ${\cal A} = \{A_1,\ldots,A_r\}$ and ${\cal B}= \{B_1,\ldots, B_s\}$ be two partitions of $V(G)$. Partition ${\cal B}$ is a refinement of partition ${\cal A}$ if every set $B_i \in {\cal B}$ is either equal to, or a proper subset of, some set $A_j \in {\cal A}$. Further if ${\cal A} \ne {\cal B}$, then ${\cal B}$ is a proper refinement of ${\cal A}$. Partition ${\cal A}$ is a minimal $c$-partition if it is not a proper refinement of another $c$-partition. Haynes et al. [AKCE Int. J. Graphs Combin. 17 (2020), no. 2, 653--659] defined the minmin coalition number $c_{\min}(G)$ of $G$ to equal the minimum order of a minimal $c$-partition of $G$. We show that $2 \le c_{\min}(G) \le n$, and we characterize graphs $G$ of order $n$ satisfying $c_{\min}(G) = n$. A polynomial-time algorithm is given to determine if $c_{\min}(G)=2$ for a given graph $G$. A necessary and sufficient condition for a graph $G$ to satisfy $c_{\min}(G) \ge 3$ is given, and a characterization of graphs $G$ with minimum degree~$2$ and $c_{\min}(G)= 4$ is provided

On the coalition number of trees

Let $G$ be a graph with vertex set $V$ and of order $n = |V|$, and let $\delta(G)$ and $\Delta(G)$ be the minimum and maximum degree of $G$, respectively. Two disjoint sets $V_1, V_2 \subseteq V$ form a coalition in $G$ if none of them is a dominating set of $G$ but their union $V_1\cup V_2$ is. A vertex partition $\Psi=\{V_1,\ldots, V_k\}$ of $V$ is a coalition partition of $G$ if every set $V_i\in \Psi$ is either a dominating set of $G$ with the cardinality $|V_i|=1$, or is not a dominating set but for some $V_j\in \Psi$, $V_i$ and $V_j$ form a coalition. The maximum cardinality of a coalition partition of $G$ is the coalition number $\mathcal{C}(G)$ of $G$. Given a coalition partition $\Psi = \{V_1, \ldots, V_k\}$ of $G$, a coalition graph \CG(G, \Psi) is associated on $\Psi$ such that there is a one-to-one correspondence between its vertices and the members of $\Psi$, where two vertices of \CG(G, \Psi) are adjacent if and only if the corresponding sets form a coalition in $G$. In this paper, we partially solve one of the open problems posed in Haynes et al. \cite{coal0} and we solve two open problems posed by Haynes et al. \cite{coal1}. We characterize all graphs $G$ with $\delta(G) \le 1$ and $\mathcal{C}(G)=n$, and we characterize all trees $T$ with $\mathcal{C}(T)=n-1$. We determine the number of coalition graphs that can be defined by all coalition partitions of a given path. Furthermore, we show that there is no universal coalition path, a path whose coalition partitions defines all possible coalition graphs

Metabolic effects of berberine on liver phosphatidate phosphohydrolase in rats fed on high lipogenic diet: An additional mechanism for the hypolipidemic effects of berberine

Objective: To evaluate the effects of berberine (BBR) on the liver phosphatidate phosphohydrolase (PAP) and plasma lipids in rats fed on high lipogenic and normal diet. Methods: Forty rats were randomly divided into 5 groups. Group I (control) received standard diet. Group II received standard diet plus 90 mg/kg BBR and Groups IV received lipogenic diet (containing sunflower oil, cholesterol and ethanol) without treatment. Groups III and V received lipogenic diet plus 90 mg/kg BBR and 30 mg/kg gemfibrozil, respectively. On Day 60 of the experiment, blood samples were collected and PAP, total cholesterol, triglyceride, low density lipoprotein cholesterol, high density lipoprotein cholesterol, very low density lipoprotein, malondialdehyde, plasma antioxidant, and liver histopathology assessments were conducted. Results: PAP, plasma triglyceride, total cholesterol, very low density lipoprotein, and malondialdehyde levels decreased significantly (P < 0.05) in Group III compared to Group IV (24 94, 36 11, 21 18, 36.86 and 19 59, respectively). The liver triglyceride and cholesterol in Groups III and V had a remarkable decrease (P < 0.001) compared with Group IV (24.94 and 49.13, respectively). There was a significant reduction (P < 0.05) in atherogenic index in Groups III compared with Group IV. Conclusions: These results clearly suggested that BBR could be effective in reducing liver PAP, lipid abnormality, liver triglyceride and lateral side effects of hyperlipidemia. © 2014 by the Asian Pacific Journal of Tropical Biomedicine

Seroprevalence and Risk Factors for Infection with Bovine Respiratory Syncytial Virus, Bovine Parainfluenza Virus-3, and Bovine Adenovirus-3 in Dairy Cattle Farms of Fars Province, Southern Iran

The seroprevalences of BRSV, BPIV-3, and BAV-3 were studied in the dairy cattle of Fars Province in the south of Iran and their associated risk factors were determined. Serum samples (n = 420) were collected from 36 cattle herds in the northern, central, and southern regions of the study area. Commercial enzyme-linked immunosorbent assay kits were used to detect antibodies against these viruses. The Chi-square test and logistic regression were used to identify potential risk factors. Antibodies were estimated 100% for all the studied viruses at the herd level and 76.43%, 76.90%, and 92.62% at the animal level for BRSV, BPIV-3, and BAV-3, respectively. In logistic regression analysis, age for all the viruses, season for BPIV-3 and BAV-3, and region and farming type for BAV-3 were significantly related to seroprevalence at the animal level. A significant association of dual infections with studied viruses was identified. The present study demonstrated that BRSV, BPIV-3, and BAV-3 are very prevalent in the dairy herds of southern Iran and highlighted the necessity to establish a control program

Dvogodišnje serološko istraživanje virusa goveđe virusne dijareje, goveđeg alfa-herpesvirusa 1 i virusa goveđe parainfluence tipa 3 na farmama mliječnih krava u Qazvinu, sjeverozapadni Iran

Infections with bovine viral diarrhea virus (BVDV), bovine alphaherpesvirus 1 (BoHV-1), and bovine parainfluenza virus type 3 (BPIV-3) cause diseases in cattle with serious economic consequences worldwide. The objective of the present study was to determine of herd-level and animal-level BVDV, BoHV-1, and BPIV-3 seroprevalence, and evaluate some of the associated risk factors on farms in Qazvin province, Northwestern Iran. A total of 1036 cattle in 16 herds were randomly selected, and their serum samples were tested to detect antibodies to these viruses in a cross-sectional study over 2 years. The results showed the seroprevalence of BVDV, BoHV-1, and BPIV-3 was 100%, 56.3%, and 100% at herd-level and 55.1%, 5.1%, and 95.2% at animal-level, respectively. Statistical analysis revealed that the farm was a strong risk factor for all the studied viruses, while the year was determined as a risk factor for only BVDV (P<0.001). The seroprevalence of BVDV and BPIV-3 was significantly (P<0.01) affected by season. The proportion of seropositive cows increased with age for BVDV and BoHV-1 (P<0.001). Concurrent infection was the highest in mixed infections with BVDV and BPIV-3 (53.2%), and there was a positive correlation between BVDV and BoHV-1 seropositivity (R2= 0.106, P<0.001). The present study shows that infections of BVDV and BPIV-3 are common in cattle in Northwestern Iran and which implies the need to implement control programs to reduce the risk of the spread of these viruses.Infekcije virusom goveđe virusne dijareje (BVDV), goveđeg alfa-herpesvirusa 1(BoHV-1) i virusa goveđe parainfluenze tipa 3 (BPIV-3) uzrokuju pobol u goveda širom svijeta, sa znatnim ekonomskim posljedicama. Cilj ovog istraživanja bio je odrediti seroprevalenciju BVDV-a, BoHV-1 i BPIV-3, na razini stada i na razini životinje, te procijeniti rizične čimbenike povezane s tim virusima na farmama u pokrajini Qazvin u sjeverozapadnom Iranu. U presječnom istraživanju, koje je trajalo više od dvije godine, nasumično je odabrano ukupno 1036 goveda iz 16 stada čiji su uzorci seruma testirani kako bi se pronašla antitijela na tri navedena virusa. Rezultati su pokazali da je seroprevalencija BVDV-a 100 %, BoHV-1 56,3 %, a BPIV-3 100 % na razini stada, dok je na razini životinje seroprevalencija BVDV-a bila 55,1 %, BoHV-1 5,1 %, a BPIV-3 95,2 %. Statistička je analiza pokazala da je farma znatan rizični čimbenik za sve istraživane viruse, dok se kombinacija godine i sezone pokazala rizičnim faktorom samo za BVDV (P < 0,001). Na seroprevalenciju BVDV-a i BPIV-3 znakovito je utjecala sezona (P < 0,01). Omjer seropozitivnih krava za BVDV i BoHV-1 znakovito je rastao s dobi (P < 0,001). Najčešća je koinfekcija bila virusima BVDV i BPIV-3 (53,2 %), a ustanovljena je i pozitivna korelacija između seropozitivnosti BVDV-a i BoHV-1 (R2 = 0,106, P < 0,001). Ovo je istraživanje pokazalo da su infekcije BVDV-om i BPIV-3 česte u goveda u sjeverozapadnom Iranu što upućuje na potrebu uvođenja programa nadzora kako bi se smanjio rizik od širenja ovih virusa

Factors Affecting Oral Health Self-Care Behaviors in Seventh Grade Students in Behbahan City: An Application of the Health Belief Model

Background: Oral and dental diseases are among the most common diseases in the world that are usually initiated in childhood and adolescence. With risk factors like those of the other important non-contagious diseases, they cause pain, discomfort, deformity, and even death. As it is preventable, the promotion of the related care behaviors by identifying the effective factors is very important. Therefore, the present study aimed to determine the factors affecting oral health self-care behaviors in seventh-grade students in Behbahan city using the health belief model.Method: This descriptive-analytical study was performed on 360 seventh-grade students in Behbahan city, Iran, through a two-stage cluster sampling. The data collection tool was a questionnaire designed based on the Health Belief Model and the DMFT checklist. The collected data were analyzed using SPSS software V. 20.Results: The results showed that the mean DMFT index and students' performance score for oral health behaviors were 2.08 and 1.76, respectively. There was a significant difference between the two genders in terms of DMFT index and performance score (P = 0.007). In this study, there was a significant relationship between oral health behaviors and perceived sensitivity, perceived severity, perceived benefits, perceived barriers, cues to action, and self-efficacy. There was also an indirect and significant relationship between perceived barriers and behavior (r = 0.271, p = 0.001).Conclusion: Based on the results of this study, the structures of the health belief model were effective on students' oral self-care behaviors. Therefore, it is recommended to focus on the mentioned structures to promote these behaviors

The duck hepatitis virus 5'-UTR possesses HCV-like IRES activity that is independent of eIF4F complex and modulated by downstream coding sequences

Duck hepatitis virus (DHV-1) is a worldwide distributed picornavirus that causes acute and fatal disease in young ducklings. Recently, the complete genome of DHV-1 has been determined and comparative sequence analysis has shown that possesses the typical picornavirus organization but exhibits several unique features. For the first time, we provide evidence that the 626-nucleotide-long 5'-UTR of the DHV-1 genome contains an internal ribosome entry site (IRES) element that functions efficiently both in vitro and in mammalian cells. The prediction of the secondary structure of the DHV-1 IRES shows significant similarity to the hepatitis C virus (HCV) IRES. Moreover, similarly to HCV IRES, DHV-1 IRES can direct translation initiation in the absence of a functional eIF4F complex. We also demonstrate that the activity of the DHV-1 IRES is modulated by a viral coding sequence located downstream of the DHV-1 5'-UTR, which enhances DHV-1 IRES activity both in vitro and in vivo. Furthermore, mutational analysis of the predicted pseudo-knot structures at the 3'-end of the putative DHV-1 IRES supported the presence of conserved domains II and III and, as it has been previously described for other picornaviruses, these structures are essential for keeping the normal internal initiation of translation of DHV-1

Characterisation of the internal ribosome entry site element from avian encephalomyelitis virus (AEV).

Avian encephalomyelitis virus (AEV) is a picornavirus that affects young chickens, quails, pheasants and turkeys. Translation initiation on picornavirus mRNA is cap independent and occurs through a mechanism known as internal initiation, which depends on Internal Ribosome Entry Site (IRES) element within the 5' untranslated region (UTR) of the viral RNA. AEV has been assigned within the Hepatovirus genus and shares protein sequence similarity with hepatitis A virus (HAV). I have demonstrated that the 494 nucleotide 5' UTR of the AEV genome contains an internal ribosome entry site (IRES) element. However, in contrast to the HAV IRES, the AEV IRES functions efficiently in the presence of cleaved eEF4G, suggesting functional differences exist. Characterization of the AEV IRES element revealed that there are remarkable structural and functional similarities between the AEV, flavivirus [especially hepatitis C virus (HCV)] and newly discovered type 4 picornaviras IRES elements, including porcine teschovirus-1 (PTV-1), porcine enterovirus-8 (PEV-8) and simian virus-2. These related IRES elements are generally shorter than other picornaviras IRES elements and are able to directly interact with 40S ribosomal subunits. These results indicate that despite classification of AEV as a Hepatovirus, the AEV IRES element should be grouped into the picornavirus type four IRES elements. Seneca Valley virus-001 (SVV) has recently been isolated from pigs and identified as a member of the Picornaviridae capable of killing tumor cells. Initial analysis of the SVV- 001 5' UTR revealed that it may contain an IRES element highly reminiscent of those of the Flaviviridae, especially classical swine fever virus (CSFV). However, further research is required to fully characterize the SVV-001 IRES element

Characterisation of the internal ribosome entry site element from avian encephalomyelitis virus (AEV).

Avian encephalomyelitis virus (AEV) is a picornavirus that affects young chickens, quails, pheasants and turkeys. Translation initiation on picornavirus mRNA is cap independent and occurs through a mechanism known as internal initiation, which depends on Internal Ribosome Entry Site (IRES) element within the 5' untranslated region (UTR) of the viral RNA. AEV has been assigned within the Hepatovirus genus and shares protein sequence similarity with hepatitis A virus (HAV). I have demonstrated that the 494 nucleotide 5' UTR of the AEV genome contains an internal ribosome entry site (IRES) element. However, in contrast to the HAV IRES, the AEV IRES functions efficiently in the presence of cleaved eEF4G, suggesting functional differences exist. Characterization of the AEV IRES element revealed that there are remarkable structural and functional similarities between the AEV, flavivirus [especially hepatitis C virus (HCV)] and newly discovered type 4 picornaviras IRES elements, including porcine teschovirus-1 (PTV-1), porcine enterovirus-8 (PEV-8) and simian virus-2. These related IRES elements are generally shorter than other picornaviras IRES elements and are able to directly interact with 40S ribosomal subunits. These results indicate that despite classification of AEV as a Hepatovirus, the AEV IRES element should be grouped into the picornavirus type four IRES elements. Seneca Valley virus-001 (SVV) has recently been isolated from pigs and identified as a member of the Picornaviridae capable of killing tumor cells. Initial analysis of the SVV- 001 5' UTR revealed that it may contain an IRES element highly reminiscent of those of the Flaviviridae, especially classical swine fever virus (CSFV). However, further research is required to fully characterize the SVV-001 IRES element

Bovine Ephemeral Fever in Iran: Diagnosis, Isolation and Molecular Characterization

Background: Bovine ephemeral fever (BEFV) is an arthropod-borne disease of cattle and water buffaloes. BEFV occurs seasonally in tropical, subtropical and temperate regions of Africa, Asia and Australia. It has been known for the past decades in Iran based on clinical signs but lack of an accurate diagnosis has made the real feature of disease obscured. This is the first scientific report on isolation and identification of the agent in which molecular diagnosis of BEFV was also set up with high sensitivity and specificity. Methods: The viral agent was successfully isolated through serial passages in brain of suckling mice and cell culture. In addition, the circulating virus during the autumn 2012 in Iran was molecularly characterized based on partial G gene. Results: Alignment of 3 virus sequences from different parts of Iran revealed that they are identical suggesting that the circulating viruses were most likely the same in this period. Phylogenetic analysis of the Iranian sequences with 17 sequences in the GenBank from the world showed that it is identical to the virus circulated in Turkey during the same period suggesting that the virus was circulated in a large geographic region. Conclusion: These results offer primary information about BEFV in Iran. To better understanding the epidemiology of the virus, further studies based on seroepidemiology, molecular epidemiology, entomology and meteorology together with finding the model of animal transportation in the region are necessary