| Adjacent Strong Edge Chromatic Number of Series-Parallel Graphs |
| Received:January 13, 2003 |
| Key Words:
series-parallel graph adjacent strong edge coloring adjacent strong edge chromatic number.
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| Fund Project:National Natural Science Foundation of China (60103021, 60274026) |
| Author Name | Affiliation | | WANG Shu-dong | College of Info. Sci. Eng., Shandong University of Sci. Technology, Tai'an 271019, China
Dept. of Control Sci. Eng., Huazhong University of Sci. Technology, Wuhan 430074, China | | PANG Shan-chen | College of Info. Sci. Eng., Shandong University of Sci. Technology, Tai'an 271019, China | | XU Jin | Dept. of Control Sci. Eng., Huazhong University of Sci. Technology, Wuhan 430074, China |
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| Abstract: |
| In this paper, we will study the adjacent strong edge coloring of series-parallel graphs, and prove that series-parallel graphs of △(G) = 3 and 4 satisfy the conjecture of adjacent strong edge coloring using the double inductions and the method of exchanging colors from the aspect of configuration property. For series-parallel graphs of △(G) ≥ 5, △(G) ≤ x′as(G) ≤△(G) + 1. Moreover, x′as(G) = △(G) + 1 if and only if it has two adjacent vertices of maximum degree, where △(G) and x′as(G) denote the maximum degree and the adjacent strong edge chromatic number of graph G respectively. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2005.02.008 |
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