NOTE ON SUPER (a,1)(a,1)–P3P_3–ANTIMAGIC TOTAL LABELING OF STAR SnS_n

Let $G=(V, E)$ be a simple graph and $H$ be a subgraph of $G$. Then $G$ admits an $H$-covering, if every edge in $E(G)$ belongs to at least one subgraph of $G$ that is isomorphic to $H$. An $(a,d)-H$-antimagic total labeling of $G$ is bijection $f:V(G)\cup E(G)\rightarrow \{1, 2, 3,\dots, |V(G)| + |E(G)|\}$ such that for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H'$ weights $w(H') =\sum_{v\in V(H')} f (v) + \sum_{e\in E(H')} f (e)$ constitute an arithmetic progression $\{a, a + d, a + 2d, \dots , a + (n- 1)d\}$, where $a$ and $d$ are positive integers and $n$ is the number of subgraphs of $G$ isomorphic to $H$. The labeling $f$ is called a super $(a, d)-H$-antimagic total labeling if $f(V(G))=\{1, 2, 3,\dots, |V(G)|\}.$ In [5], David Laurence and Kathiresan posed a problem that characterizes the super $(a, 1)-P_{3}$-antimagic total labeling of Star $S_{n},$ where $n=6,7,8,9.$  In this paper, we completely solved this problem

Note on Super (A,1)–P3–Antimagic Total Labeling of Star Sn

Let G=(V,E) be a simple graph and H be a subgraph of G. Then G admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a,d)−H-antimagic total labeling of G is bijection f:V(G)∪E(G)→{1,2,3,…,|V(G)|+|E(G)|} such that for all subgraphs H′ of G isomorphic to H, the H′ weights w(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constitute an arithmetic progression {a,a+d,a+2d,…,a+(n−1)d}, where a and d are positive integers and n is the number of subgraphs of G isomorphic to H. The labeling f is called a super (a,d)−H-antimagic total labeling if f(V(G))={1,2,3,…,|V(G)|}. In [5], David Laurence and Kathiresan posed a problem that characterizes the super (a,1)−P3-antimagic total labeling of Star Sn, where n=6,7,8,9. In this paper, we completely solved this problem.The authors are thankful to there viewers for helpful suggestions which led to substantial improvement in the presentation of the paper

Complete characterization of s-bridge graphs with local antimagic chromatic number 2

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all the edges incident to $x$. The local antimagic chromatic number of $G$, denoted by $\chi_{la}(G)$, is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G$. In this paper, we characterize $s$-bridge graphs with local antimagic chromatic number 2

Could dental school teaching clinics provide better care than regular private practices?

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149321/1/jicd12329.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149321/2/jicd12329_am.pd

Acute dental infections managed in an outpatient parenteral antibiotic program setting: prospective analysis and public health implications

BACKGROUND: The number of Acute Dental Infections (ADI) presenting for emergency department (ED) care are steadily increasing. Outpatient Parenteral Antibiotic Therapy (OPAT) programs are increasingly utilized as an alternative cost-effective approach to the management of serious infectious diseases but their role in the management of severe ADI is not established. This study aims to address this knowledge gap through evaluation of ADI referrals to a regional OPAT program in a large Canadian center. METHODS: All adult ED and OPAT program ADI referrals from four acute care adult hospitals in Calgary, Alberta, were quantified using ICD diagnosis codes in a regional reporting system. Citywide OPAT program referrals were prospectively enrolled over a five-month period from February to June 2014. Participants completed a questionnaire and OPAT medical records were reviewed upon completion of care. RESULTS: Of 704 adults presenting to acute care facilities with dental infections during the study period 343 (49%) were referred to OPAT for ADI treatment and 110 were included in the study. Participant mean age was 44 years, 55% were women, and a majority of participants had dental insurance (65%), had seen a dentist in the past six months (65%) and reported prior dental infections (77%), 36% reporting the current ADI as a recurrence. Median length of parenteral antibiotic therapy was 3 days, average total course of antibiotics was 15-days, with a cumulative 1326 antibiotic days over the study period. There was no difference in total duration of antibiotics between broad and narrow spectrum regimes. Conservative cost estimate of OPAT care was $120,096, a cost savings of$597,434 (83%) compared with hospitalization. CONCLUSIONS: ADI represent a common preventable cause of recurrent morbidity. Although OPAT programs may offer short-term cost savings compared with hospitalization, risks associated with extended antibiotic exposures and delayed definitive dental management must also be gauged. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12879-017-2303-2) contains supplementary material, which is available to authorized users

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Local total anti-magic chromatic number of graphs

Let G=(V,E) be a graph without isolated vertices and let |V(G)|=n and |E(G)|=m. A bijection π:V(G)∪E(G)→{1,2,....,n+m} is said to be local total anti-magic labeling of a graph G if it satisfies the conditions: (i.) for any edge uv, ω(u)≠ω(v), where u and v in V(G) (ii.) for any two adjacent edges e and e′, ω(e)≠ω(e′) (iii.) for any edge uv∈E(G) is incident to the vertex v, ω(v)≠ω(uv), where weight of vertex u is, ω(u)=∑e∈S(u)π(e), S(u) is the set of edges with every edge of S(u) one end vertex is u and an edge weight is ω(e=uv)=π(u)+π(v). In this paper, we have introduced a local total anti-magic labeling (LTAL) and the local total anti-magic chromatic number (LTACN). Also, we obtain the LTACN for the graphs Pn, K1,n, Fn and Sn,n