Transitivity on subclasses of chordal graphs

Let $G=(V, E)$ be a graph, where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \textit{dominates} $B$ if every vertex of $B$ is adjacent to at least one vertex of $A$ in $G$. A vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ of $G$ is called a \emph{transitive $k$-partition} if $V_i$ dominates $V_j$ for all $i,j$, where $1\leq i<j\leq k$. The maximum integer $k$ for which the above partition exists is called \emph{transitivity} of $G$ and it is denoted by $Tr(G)$. The \textsc{Maximum Transitivity Problem} is to find a transitive partition of a given graph with the maximum number of partitions. It was known that the decision version of \textsc{Maximum Transitivity Problem} is NP-complete for chordal graphs [Iterated colorings of graphs, \emph{Discrete Mathematics}, 278, 2004]. In this paper, we first prove that this problem can be solved in linear time for \emph{split graphs} and for the \emph{complement of bipartite chain graphs}, two subclasses of chordal graphs. We also discuss Nordhaus-Gaddum type relations for transitivity and provide counterexamples for an open problem posed by J. T. Hedetniemi and S. T. Hedetniemi [The transitivity of a graph, \emph{J. Combin. Math. Combin. Comput}, 104, 2018]. Finally, we characterize transitively critical graphs having fixed transitivity.Comment: arXiv admin note: text overlap with arXiv:2204.1314

INDUCTION OF APOPTOSIS BY FATTY ACID RICH FRACTION OF SOLANUM NIGRUM ON CERVICAL CANCER CELL LINES

Objective: Mechanism of cell death inducing pathway of chloroform fraction of methanolic extract of Solanum nigrum were studied in a panel of cervical cancer cell line.Methods: Cells were treated with IC50 doses (previously determined by MTT assay), and various experiments were performed. For cellular and nuclear morphology, cells were stained with Hoechst33258 and observed under phase and fluorescence microscopy. Cell cycle shift and apoptotic assay (AnnexinV-FITC/PI) were studied by flow cytometry. Expressions of relevant genes were studied at the transcriptional and translational levels. ROS induction and loss of MMP and presence of γH2AX were studied by fluorescent microscopy. Constituents of the fraction were separated by column chromatography and bioassayed by MTT assay. Bioactive sub-fractions were identified by GC-MS.Results: Typical apoptotic morphological features were found in the treated cells. Most cells were found in late apoptotic stages. In HeLa and C33A cell lines, cells were blocked at G1/S, in SiHa, subG0 population increased. Expression of antiapoptotic Bcl-2 decreased and that of proapoptotic BAX, p53, p21 increased. Expression of HPV16 and human ET1 also decreased. ROS mediated DNA damage was detected and induced apoptosis. Different fatty acids along with other compounds were detected in the chloroform fraction, all of which are reported to have anticancer properties.Conclusion: From the study it can be concluded that fatty acid rich chloroform fraction of S. nigrum is capable of inducing apoptosis in cervical cancer cells, through ROS mediated DNA damage

Algorithmic study on 22-transitivity of graphs

Let $G=(V, E)$ be a graph where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \emph{dominates} $B$ if every vertex of $B$ is adjacent to at least one vertex of $A$. A vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ of $G$ is called a \emph{transitive partition} of size $k$ if $V_i$ dominates $V_j$ for all $1\leq i<j\leq k$. In this article, we study a variation of transitive partition, namely \emph{$2$-transitive partition}. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \emph{$2$-dominates} $B$ if every vertex of $B$ is adjacent to at least two vertices of $A$. A vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ of $G$ is called a \emph{$2$-transitive partition} of size $k$ if $V_i$ $2$-dominates $V_j$ for all $1\leq i<j\leq k$. The \textsc{Maximum $2$-Transitivity Problem} is to find a $2$-transitive partition of a given graph with the maximum number of parts. We show that the decision version of this problem is NP-complete for chordal and bipartite graphs. On the positive side, we design three linear-time algorithms for solving \textsc{Maximum $2$-Transitivity Problem} in trees, split and bipartite chain graphs

INDUCTION OF AUTOPHAGY IN HUMAN CERVICAL CANCER CELL LINE (SIHA) BY CHAETOMORPHA LINUM (MULLER) KÃœTZ.

Objective: Algae is a rich source of various metabolites. Use of algae in traditional medicine was reported from very early days. The potential anticancerous activity of the algae was also reported by recent researches. In the present study, cell death mechanism induced by green alga Chaetomorpha linum (Muller) Kütz. was studied on human cervical cancer cell line, SiHa (Human papilloma virus-HPV 16+ve).Methods: Cells were treated with chloroform fraction of the Chaetomorpha linum (CLC). DNA fragmentation, cell proliferation, nuclear morphology, localization of autophagosomes and expression of relevant proteins were studied. Cell cycle and mitochondrial membrane potential (MMP) were assessed by fluorescence assisted cell sorting (FACS). Gas chromatography liquid spectrometry (GCMS) analysis of CLC was done to detect the algal compounds.Results: Preliminary experiments confirmed the absence of DNA fragmentation and altered nuclear morphology in the treated cells. In the Acridine Orange stained cells, the presence of autophagosomes was observed by both microscopy and FACS analysis. Decreased MMP was observed in the treated sets. Wound healing assay showed the inhibitory activity of CLC on SiHa cells. Increased expression of autophagic proteins, viz; LC3BII, p62/SQSTM, Beclin-1 and decreased expression of S6 were observed in the treated sets; indicating that autophagic cell death was induced. Preliminary qualitative chemical study and GCMS analysis detected the presence of saponins, glycosides, alkaloids, phenols, steroids and fatty acids in CLC.Conclusion: All these findings clearly suggested that the chloroform fraction of the algae was responsible for induction of apoptosis followed by autophagic cell death in SiHa and can serve as a potential candidate for anticancer drug development in future

Nanoparticles mediated cadmium toxicity amelioration in plants

Application of nanoparticles to address various environmental issues; especially heavy metal contaminated soil restoration is of global interest. Indiscriminate usage of phosphate fertilizer and other anthropogenic activities contribute to Cd contamination of soil, resulting in degradation of soil quality and low crop yield. By the virtue of unique physiochemical characteristics, nanoparticles (NPs) are effective enough for heavy metal stress mitigation. This review has focused on Cd uptake, accumulation and toxicity in plants followed by the successful application of different metallic and non metallic NPs for soil Cd decontamination. Positive impact of NPs as plant growth elicitor under Cd stress has been explored here. Various ways of NP application (soil, foliar, hydroponics), uptake, mode of action and effective treatment concentration have been highlighted. We have collected handful information regarding the use of NPs as nanofertilizer and nanopesticides. The negative effects of NPs have not been considered here. More in depth study to be conducted for better illumination on plant - NPs interaction, mobilization mechanism and biological activities. Though this review summarizes few facts among various aspect of NP but can be counted as a supportive documentation for the better use of NPs in environmental protection in future

A Direct Construction of Optimal Symmetrical Z-Complementary Code Sets of Prime Power Lengths

This paper presents a direct construction of an optimal symmetrical Z-complementary code set (SZCCS) of prime power lengths using a multi-variable function (MVF). SZCCS is a natural extension of the Z-complementary code set (ZCCS), which has only front-end zero correlation zone (ZCZ) width. SZCCS has both front-end and tail-end ZCZ width. SZCCSs are used in developing optimal training sequences for broadband generalized spatial modulation systems over frequency-selective channels because they have ZCZ width on both the front and tail ends. The construction of optimal SZCCS with large set sizes and prime power lengths is presented for the first time in this paper. Furthermore, it is worth noting that several existing works on ZCCS and SZCCS can be viewed as special cases of the proposed construction