Clique-transversal sets of line graphs and complements of line graphs
نویسندگان
چکیده
منابع مشابه
Clique-perfectness of complements of line graphs
The clique-transversal number τc(G) of a graph G is the minimum size of a set of vertices meeting all the cliques. The clique-independence number αc(G) of G is the maximum size of a collection of vertex-disjoint cliques. A graph is clique-perfect if these two numbers are equal for every induced subgraph of G. Unlike perfect graphs, the class of clique-perfect graphs is not closed under graph co...
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The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
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A clique-transversal set S of a graph G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted τc(G), is the minimum cardinality of a clique-transversal set in G. In this paper we present an upper bound and a lower bound on τc(G) for cubic graphs, and characterize the extremal cubic graphs achieving the lower bound. In addition, we present a sharp u...
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The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملClique coverings and partitions of line graphs
A clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a collection C of cliques such that each edge of G occurs in at least (exactly) one clique in C. The clique covering (partition) number cc(G) (cp(G)) of G is the minimum size of a clique covering (partition) of G. This paper gives alternative proofs, using a unified approach, for the results on the clique c...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90055-7