On the Adjacent Strong Edge Coloring of Outer Plane Graphs |
Received:February 09, 2003 |
Key Words:
outer plane graph vertex distinguishing edge coloring adjacent strong edge coloring.
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Fund Project:National Natural Science Foundation of China (No.19871036) and Qinglan talent Funds of Lanzhou Jiaotong University. |
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Abstract: |
A k-adjacent strong edge coloring of graph G(V, E) is defined as a proper kedge coloring f of graph G(V, E) such that f[u] ≠ f[v] for every uv ∈ E(G), where f[u] ={f(uw)|uw ∈ E(G)} and f(uw) denotes the color of uw, and the adjacent strong edge chromatic number is defined as x′as(G) = min{k| there is a k-adjacent strong edge coloring of G}. In this paper, it has been proved that △≤ x′as(G) ≤△ + 1 for outer plane graphs with △(G) ≥ 5, and x′as(G) = △ + 1 if and only if there exist adjacent vertices with maximum degree. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2005.02.007 |
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