منابع مشابه
Irregular colorings of regular graphs
An irregular coloring of a graph is a proper vertex coloring that distinguishes vertices in the graph either by their own colors or by the colors of their neighbors. In algebraic graph theory, graphs with a certain amount of symmetry can sometimes be specified in terms of a group and a smaller graph called a voltage graph. In [3], Radcliffe and Zhang found a bound for the irregular chromatic nu...
متن کاملOn Irregular Colorings of Graphs
For a graph G and a proper coloring c : V (G) → {1, 2, . . . , k} of the vertices of G for some positive integer k , the color code of a vertex v of G (with respect to c ) is the ordered (k + 1) -tuple code(v) = (a0, a1, . . . , ak) where a0 is the color assigned to v and for 1 ≤ i ≤ k , ai is the number of vertices adjacent to v that are colored i . The coloring c is irregular if distinct vert...
متن کاملInterference-Minimizing Colorings of Regular Graphs
Communications problems that involve frequency interference, such as the channel assignment problem in the design of cellular telephone networks, can be cast as graph coloring problems in which the frequencies (colors) assigned to an edge’s vertices interfere if they are too similar. The paper considers situations modeled by vertex-coloring d-regular graphs with n vertices using a color set {1,...
متن کاملOn b-colorings in regular graphs
A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes. El-Sahili and Kouider have conjectured that every d-regular graph with girth at least 5 has a b-coloring with d+1 colors. We show that the Petersen graph infirms this conjecture, and we propose a new formulation of this question and give a positive a...
متن کاملRandom Walks on Regular and Irregular Graphs
For an undirected graph and an optimal cyclic list of all its vertices, the cyclic cover time is the expected time it takes a simple random walk to travel from vertex to vertex along the list, until it completes a full cycle. The main result of this paper is a characterization of the cyclic cover time in terms of simple and easy to compute graph properties. Namely, for any connected graph, the ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.03.039