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On Edge Cover Colorings of Graphs

Author: DuHongMei
Tutor: XuChangQing
School: Hebei University of Technology
Course: Applied Mathematics
Keywords: Halin graph edge cover-coloring edge cover chromaticindex edge cover critical graph
CLC: O157.5
Type: Master's thesis
Year: 2010
Downloads: 16
Quote: 1
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Abstract


Let G(V,E) be a simple graph with edge set E(G) and vertex set V (G).A mapping C of G from E(G) to a color set{1，2,…，K} is called a h-edge-coloring of G. Let (i) denote the number of edges of G incident withvertex:receiving color i by the coloringC .If for each ,and {1, 2,…，k}, C is called a h-edge cover-coloring of G. Let (G)be the maximum positive integer h for which an h-edge cover-coloring ofG exists. Then (G) is called the edge cover chromatic index of G. Itis known that G is a graph of CIclass, otherwise G is a graph of CII class. In this paper，we consider theclassification of Halin graphs based on the edge cover chromatic index. Weobtain a necessary and sufficient condition for some Hafin graphs to be ofclass CI; We also obtain a property of edge cover critical graphs.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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