Twin Edge Coloring of Graphs

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Fereydounian, Mohammad | 2016

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 48698 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saeed
Abstract:
Let G be a graph. A twin edge k-coloring of G is a proper edge coloring of G with the elements of Z_k so that for every vertex u and v of G we have s(u)≠s(v), where s(u) is the sum of all colors of the edges incident with u. The minimum k for which G has a twin edge k-coloring is called twin chromatic index of G and denoted by χ_t^' (G). In this thesis we find the chromatic index of paths, cycles, complete graphs, complete bipartite graphs and some complete tripartite graphs. In 2014 it was conjectured that if G is a connected graph with at least 3 vertices and maximum degree Δ(G), then χ_t^' (G)≤Δ(G)+3
Keywords:
Factorization Method ; Bipartite Graph ; Twin Edge Coloring ; Graceful Tree ; Proper Edge Coloring