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PresentationsSum Edge-colorings of Some Complete Tripartite and Some Regular GraphsYerevan State University, 1 Alex Manoogian St., Yerevan, 0025, Armenia, hamlet.miqayelyan@ysu.am, petros_petrosyan@ysu.am A proper edge-coloring of a graph is called a sum edge-coloring if it minimizes the total sum of colors on all the edges of the graph (defined by Bar-Noy et al. in 1998, [1]). The aforementioned minimal sum is called the edge-chromatic sum of the graph $G$ and is denoted by $\Sigma'(G)$, and the minimal number of colors needed for a sum edge-coloring is called the edge-strength of the graph $G$ and is denoted by $s'(G)$. In this work, we have obtained the exact values of the edge-chromatic sums and the edge-strength of some complete tripartite graphs. We have also given the values of both parameters for some generalization of cycles $C_n(m)$ defined by Parker in 1973 ([2]).
References. 1. Bar-Noy A., Bellare M., Halldórsson M.M., Shachnai H., and Tamir T. On chromatic sums and distributed resource allocation // Information and Computation. Vol. 140, No. 2, 1998. Pp. 183-202. 2. Parker E.T. Edge coloring numbers of some regular graphs // Proceedings of the American Mathematical Society. Vol. 37, No. 2, 1973. Pp. 423-424.
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