On subgraphs of tripartite graphs

A generalization of Villarreal's result for unmixed tripartite graphs

‎In this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of Villarreal on bipartite graphs‎. ‎For bipartite graphs two‎ ‎different characterizations were given by Ravindra and Villarreal‎. ‎We show that these two characterizations imply each other‎.

TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the numbe...

On Cyclic Decompositions of Complete Graphs into Tripartite Graphs

We introduce two new labelings for tripartite graphs and show that if a graph G with n edges admits either of these labelings, then there exists a cyclic G-decomposition of K2nx+1 for every positive integer x. We also show that if G is the union of two vertext-disjoint cycles of odd length, other than C3 ∪ C3, then G admits one of these labelings.

On K4-Free Subgraphs of Random Graphs

On Complete Topological Subgraphs of Certain Graphs

Let G he a graph . We say that G contains a complete k-gon if there are !c vertices of G any two of which are connected by an edge, we say that it contains a complete topological k-gon if it contains k vertices any two of which are connected by paths no two of which have a common vertex (except endpoints) . Following G . DIRAC we will denote complete k-gons by -k = and complete topological k-go...