Operations Research Transactions
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LV Xuezheng1 WEI Erling1,* SONG Hongye2
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In 1937 MacLane gave the important theory on cycle basis: gaph G is planar if and only if G has a 2-basis. The join G = G_1\vee G_2 of graphs G_1 and G_2 is obtained from G_1\bigcup G_2 by adding all the edges in {(u,v)|u\in V(G_1), v\in V(G_2)}. In this paper we investigate the basis number of G = G_1\vee G_2 and obtain an upper bound which improves the bound given by Zare. Based on this, a better bound of C_m \vee C_n is derived too.
Key words: join of graph, cycle space, basis
LV Xuezheng, WEI Erling, SONG Hongye. The basis number of join graphs[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2018.04.015.
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URL: https://www.ort.shu.edu.cn/EN/10.15960/j.cnki.issn.1007-6093.2018.04.015
https://www.ort.shu.edu.cn/EN/Y2018/V22/I4/148