منابع مشابه
Lexicographic Product of Extendable Graphs
Lexicographic product G◦H of two graphs G and H has vertex set V (G)×V (H) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1u2 ∈ E(G), or u1 = u2 and v1v2 ∈ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the l...
متن کاملIdentifying Codes of Lexicographic Product of Graphs
Let G be a connected graph and H be an arbitrary graph. In this paper, we study the identifying codes of the lexicographic product G[H] of G and H. We first introduce two parameters of H, which are closely related to identifying codes of H. Then we provide the sufficient and necessary condition for G[H] to be identifiable. Finally, if G[H] is identifiable, we determine the minimum cardinality o...
متن کاملNonrepetitive colorings of lexicographic product of graphs
A coloring c of the vertices of a graph G is nonrepetitive if there exists no path v1v2 . . . v2l for which c(vi) = c(vl+i) for all 1 ≤ i ≤ l. Given graphs G and H with |V (H)| = k, the lexicographic product G[H ] is the graph obtained by substituting every vertex of G by a copy of H , and every edge of G by a copy of Kk,k. We prove that for a sufficiently long path P , a nonrepetitive coloring...
متن کاملConnectivity of lexicographic product and direct product of graphs
In this paper, we prove that the connectivity and the edge connectivity of the lexicographic product of two graphs G1 and G2 are equal to κ1v2 and min{λ1v 2 2 , δ2 +δ1v2}, respectively, where δi, κi, λi and vi denote the minimum degree, the connectivity, the edge-connectivity and the number of vertices of Gi, respectively. We also obtain that the edge-connectivity of the direct product of K2 an...
متن کاملOn the b-continuity of the lexicographic product of graphs
A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to each other color class. The b-chromatic number of G is the maximum integer χb(G) for which G has a b-coloring with χb(G) colors. A graph G is b-continuous if G has a b-coloring with k colors, for every integer k in the interval [χ(G), χb(G)]. It is known that not all graphs...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2019
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2243