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研究生:王禕祺
研究生(外文):Wang, YiChi
論文名稱:均勻符號圖之邊多數指數研究
論文名稱(外文):Study of Edge-Majority Indices of Equitable Signed Graphs
指導教授:王道明
指導教授(外文):Tao-Ming Wang
口試委員:黃國卿陳伯亮
口試日期:2012-06-15
學位類別:碩士
校院名稱:東海大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:27
外文關鍵詞:Edge-Majority IndexEquitable Signed Graph
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Let G be a connected multi-graph with vertex set V (G) and edge set E(G).
If there exists an edge labeling function f from E(G) to {1,-1}, such that the
difference of numbers of edges labeled 1 and -1 is at most one, then we call
such f an equitable labeling and G an equitable signed graph.
An equitable edge labeling induces a vertex labeling in the following way. For
vertices incident with more 1-edges than (-1)-edges, we label them 1. For
vertices incident with more (-1)-edges than 1-edges, we label them -1. For
vertices incident with the same number of (-1)-edges and 1-edges, we label
them 0. Then the edge-majority index is de ned as the absolute di erence
of the number of 1-vertices and the number of (-1)-vertices with respect to
an equitable edge labeling. The set of all possible edge-majority indices of G
with respect to all possible equitable labelings is called the edge-majority
index set of G. Given an equitable edge labeling f of a graph with all
odd degrees(all even degrees), we show that all even numbers(all numbers)
less than certain edge-majority index with respect to f may be realized by
continuously switching edge labels.
1 Introduction
1.1 De nitions
1.2 Background
1.3 Motivation
2 Edge-Majority Indices of Odd Graphs
2.1 Basics
2.2 Main Result
3 Edge-Majority Indices of Even Graphs
3.1 Basics
3.2 Main Result
4 Conclusion and Further Studies
[1] D. Cartwright and F. Harary, Structural balance: a generalization of
Heider's theory. Psychological Review 63 (1956), 277-293.
[2] B.-L. Chen, K.-C. Huang, S.-M. Lee, and S.-S. Liu, On edge-balanced
multigraphs, Journal of Combinatorial Mathematics and Combinatorial
Computing, 42(2002), 177-185.
[3] Tao-Ming Wang, Chia-Min Lin, and Midge Cozzens, Edge Control in
Signed Graphs. Manuscript, 2010.
[4] Elliot Kropa, Sin-Min Lee, Christopher Raridan, On the number of unla-
beled vertices in edge-friendly labelings of graphs. Discrete Mathematics
312 (2012), 574-577.
[5] Rosa, A. (1967), On certain valuations of the vertices of a graph, Theory
of Graphs (Internat. Sympos., Rome, 1966), New York: Gordon and
Breach, pp. 349-355, MR 0223271.
[6] D. Chopra, S-M. Lee and H-H. Su, On edge-balance index sets of wheels,
Int. J. of Contemp. Math. Sci., 5 (2010), no. 53, 2605-2620.
[7] D. Chopra, S-M. Lee and H-H. Su, On edge-balance index sets of the
fans and broken fans, Congr. Numer., 196 (2009), 183-201.
[8] M.C. Kong, S-M. Lee and Y.C.Wang, On edge-balance index sets of
some complete k-partite graphs, Congr. Numer., 196 (2009), 71-94.
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