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Point-distinguishing chromatic index of the union of paths

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Abstract

Let G be a simple graph. For a general edge coloring of a graph G (i.e., not necessarily a proper edge coloring) and a vertex v of G, denote by S(v) the set (not a multiset) of colors used to color the edges incident to v. For a general edge coloring f of a graph G, if S(u) ≠ S(v) for any two different vertices u and v of G, then we say that f is a point-distinguishing general edge coloring of G. The minimum number of colors required for a point-distinguishing general edge coloring of G, denoted by χ0(G), is called the point-distinguishing chromatic index of G. In this paper, we determine the point-distinguishing chromatic index of the union of paths and propose a conjecture.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, 730070, P.R.China

    Xiang’en Chen

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  1. Xiang’en Chen
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Correspondence to Xiang’en Chen.

Additional information

The research has been supported by the National Natural Science Foundation of China (Grant No. 61163037, 61163054)

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Chen, X. Point-distinguishing chromatic index of the union of paths. Czech Math J 64, 629–640 (2014). https://doi.org/10.1007/s10587-014-0123-8

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  • DOI: https://doi.org/10.1007/s10587-014-0123-8

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