Edge-Coloring Vertex-Weighting of Graphs

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SHIU WAI CHEE; LAU GEE CHOON; N.G. HO KUEN

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2021 | Volume:16 | Issue:1 Page(s): 1-13

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Title

Edge-Coloring Vertex-Weighting of Graphs

Author(s)

SHIU WAI CHEE | LAU GEE CHOON | N.G. HO KUEN | Issue Writer Certificate

Keywords

Edge coloring

Vertex weighting

Abstract

Let G = (V (G), E(G)) be a simple, finite and undirected graph of order n. A k-Vertex weighting of a graph G is a mapping w: V (G) → {1, . . ., k}. A k-Vertex weighting induces an edge labeling fw: E(G) → N such that fw(uv) = w(u) + w(v). Such a labeling is called an edge-coloring k-Vertex weighting if fw(e) ̸ = fw(e′ ) for any two adjacent edges e and e′ . Denote by μ ′ (G) the minimum k for G to admit an edge-coloring k-Vertex weighting. In this paper, we determine μ ′ (G) for some classes of graphs.

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APA: Copy

SHIU, WAI CHEE, LAU, GEE CHOON, & N.G., HO KUEN. (2021). Edge-Coloring Vertex-Weighting of Graphs. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 16(1), 1-13. SID. https://sid.ir/paper/775388/en

Vancouver: Copy

SHIU WAI CHEE, LAU GEE CHOON, N.G. HO KUEN. Edge-Coloring Vertex-Weighting of Graphs. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2021;16(1):1-13. Available from: https://sid.ir/paper/775388/en

IEEE: Copy

WAI CHEE SHIU, GEE CHOON LAU, and HO KUEN N.G., “Edge-Coloring Vertex-Weighting of Graphs,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 16, no. 1, pp. 1–13, 2021, [Online]. Available: https://sid.ir/paper/775388/en

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