ON SUM EDGE-COLORINGS OF SOME REGULAR GRAPHS
Hamlet V. Mikaelyan
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Source: Crossref
Published: Apr 3, 2026
DOI: 10.46991/pysua.2026.60.1.014
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A sum edge-coloring of a graph is an assignment of positive integers to the edges of the graph, so that adjacent edges correspond to different numbers (colors) and the sum of the numbers on all the edges is minimum possible. This minimum possible sum is called the edge-chromatic sum of the graph, and the minimal number of colors needed for a sum edge-coloring is called the edge-strength of the graph. In this paper, we give the exact values of the edge-chromatic sums and edge-strengths for cycle powers and generalized cycles.
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