Abstract
Let G(V,E) be a graph. A k-adjacent vertex-distinguishing equatable edge coloring of G, k-AVEEC for short, is a proper edge coloring f if (1) C(u) ≠ C(v) for ∨uv ∈ E(G), where C(u) = {f(uv)|uv ∈ E}, and (2) for any i, j = 1, 2, … k, we have ‖E i | − |E j ‖ ≤ 1, where E i = {e|e ∈ E(G) and f(e) = i}. χ′ ave (G) =min{k| there exists a k-AVEEC of G} is called the adjacent vertex-distinguishing equitable edge chromatic number of G. In this paper, we obtain the χ′ ave (G) of some special graphs and present a conjecture.
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Supported by the National Natural Science Foundation of China (No. 10771091No.61163010) and Ningxia University Science Research Foundation (No.(E)ndzr09-15).
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Li, Jw., Wang, C. & Wang, Zw. On the adjacent vertex-distinguishing equitable edge coloring of graphs. Acta Math. Appl. Sin. Engl. Ser. 29, 615–622 (2013). https://doi.org/10.1007/s10255-013-0239-x
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DOI: https://doi.org/10.1007/s10255-013-0239-x
Keywords
- graph
- adjacent vertex-distinguishing edge coloring
- adjacent vertex-distinguishing equitable edge coloring