Rainbow Mean Colorings of Bipartite Graphs
Bulletin of the Institute of Combinatorics and its Applications
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For an edge coloring c of a connected graph G with positive integers where adjacent edges may be colored the same, the chromatic mean of a vertex v of G is the average of the colors of the edges incident with v. Only those edge colorings c for which the chromatic mean of every vertex is a positive integer are considered. If distinct vertices have distinct chromatic means, then c is a rainbow mean coloring of G. The maximum vertex color in a rainbow mean coloring c of G is the rainbow mean index of c, while the rainbow mean index of G is the minimum rainbow mean index among all rainbow mean colorings of G. The rainbow mean index of several bipartite graphs are determined, namely prisms, hypercubes, and complete bipartite graphs.
Bipartite graphs; Edge coloring; Vertex color; Rainbow mean index
Mathematics | Physical Sciences and Mathematics
Rainbow Mean Colorings of Bipartite Graphs.
Bulletin of the Institute of Combinatorics and its Applications, 88