منابع مشابه
2-Distance Colorings of Integer Distance Graphs
A 2-distance k-coloring of a graph G is a mapping from V (G) to the set of colors {1, . . . , k} such that every two vertices at distance at most 2 receive distinct colors. The 2-distance chromatic number χ2(G) of G is then the mallest k for which G admits a 2-distance k-coloring. For any finite set of positive integers D = {d1, . . . , dk}, the integer distance graph G = G(D) is the infinite g...
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Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
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The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...
متن کامل2-distance Coloring of Sparse Graphs
A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most 2 receive distinct colors. We prove that every graph with maximum degree Δ at least 4 and maximum average degree less that 73 admits a 2-distance (Δ + 1)-coloring. This result is tight. This improves previous known results of Dolama and Sopena.
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2017
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2016-071-6