Twin Edge Coloring of Graphs, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
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
Cataloging briefTwin Edge Coloring of Graphs, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
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
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