On the Adjacent Vertex Distinguishing Proper Edge Colorings of Several Classes of Complete 5-Partite Graphs

Abstract:

A proper $k$-edge coloring of a graph $G$ is an assignment of $k$ colors, $1,2,\cdots,k$, to edges of $G$. For a proper edge coloring $f$ of $G$ and any vertex $x$ of $G$, we use $S(x)$ denote the set of thecolors assigned to the edges incident to $x$. If for any two adjacent vertices $u$ and $v$ of $G$, we have $S(u)\neq S(v)$,then $f$ is called the adjacent vertex distinguishing proper edge coloring of $G$ (or AVDPEC of $G$ in brief). The minimum number of colors required in an AVDPEC of $G$ is called the adjacent vertex distinguishing proper edge chromatic number of $G$, denoted by $\chi^{'}_{\mathrm{a}}(G)$. In this paper, adjacent vertex distinguishing proper edge chromatic numbers of several classes of complete 5-partite graphs are obtained.

• Periodical: Applied Mechanics and Materials (Volumes 333-335)
• Pages: 1452-1455
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.333-335.1452
• Online since: July 2013
• Authors: Chun Yan Ma, Xiang En Chen, Fang Yang, Bing Yao
• Keywords: Adjacent Vertex Distinguishing Proper Edge Coloring, Complete 5-Partite Graphs, Proper Edge Coloring

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