On the adjacent vertex distinguishing proper edge colorings of several classes of complete 4-partite and 5-partite graphs
Chen Xiang-en, Chunyan Ma, Fang Chun Yang, Bing Yao · Proceedings of the 2nd International Symposium on Computer, Communication, Control and Automation · 2013
A proper k-edge coloring of a graph G is an assignment of k colors, 1, 2, • • • , 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 the colors assigned to the edges incident to x.If for any two adjacent vertices u and v of G, we have S(u) ̸ = 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 χ ′ a (G).In this paper, adjacent vertex distinguishing proper edge chromatic numbers of several classes of complete 4-partite and 5-partite graphs are obtained.(