# Chromatic Number of ISK4-Free Graphs

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In this paper, we continue the study of semitotal domination in graphs in [Discrete Math. 324, 13-18 (2014)]. A set $${S}$$ of vertices in $${G}$$ is a semitotal dominating set of $${G}$$ if it is a dominating set of $${G}$$ and every vertex in $${S}$$ is within distance 2 of another vertex of...

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Let n be any positive integer and Fn be the friendship (or Dutch windmill) graph with 2n+1 vertices and 3n edges. Here we study graphs with the same adjacency spectrum as Fn. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let G be a graph...

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Let G = (V,E) be a graph without isolated vertices. A dominating set S of G is called a neighborhood total dominating set (or just NTDS) if the induced subgraph G[N(S)] has no isolated vertex. The minimum cardinality of a NTDS of G is called the neighborhood total domination number of G and is...

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For a graph $$H$$ with at most $$n$$ vertices and a weighing of the edges of $$K_n$$ with integers, we seek a copy of $$H$$ in $$K_n$$ whose weight is minimal, possibly even zero. Of a particular interest are the cases where $$H$$ is a spanning subgraph (or an almost spanning subgraph) and the...

- Around The Berge Problem And Hadwiger Conjecture. Nemron, Ikorong Anouk Gilbert // International Journal of Mathematical Combinatorics;Jul2012, Vol. 3, p72
We say that a graph B is berge, if every graph B' âˆˆ {B,BÌ„} does not contain an induced cycle of odd length â‰¥ 5 [BÌ„ is the complementary graph of B]. A graph G is perfect if every induced subgraph G' of G satisfies Ï‡(G ) = Ï‰(G ), where Ï‡(G') is the chromatic number...