Sufficient conditions on the zeroth-order general Randić index for maximally edge-connected graphs

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• 作者：Zhibing Chen^a ; ^{chenzb@szu.edu.cn} ; Guifu Su^b ; ^{gfs1983@126.com} ; Lutz Volkmann^c ; ^{volkm@math2.rwth-aachen.de}
• 关键词：Edge-connectivity ; Maximal edge-connected graphs ; Zeroth-order general Randić index
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：19 February 2017
• 年：2017
• 卷：218
• 期：Complete
• 页码：64-70
• 全文大小：393 K
• 卷排序：218

文摘

Let GG be a connected graph with vertex set VV, minimum degree δδ and edge-connectivity λλ. If αα is a real number, then the zeroth-order general Randić index is defined by ∑x∈Vdegα(x), where deg(x) denotes the degree of the vertex xx. A graph is maximally edge-connected if λ=δλ=δ. In this paper, we present sufficient conditions for connected graphs (resp. connected triangle-free graphs) to be maximally edge-connected in terms of the zeroth-order general Randić index, the order and the minimum degree when α∈(−∞,0)α∈(−∞,0) or α∈(1,2]α∈(1,2] (resp. α∈[−1,0)∪(1,2]α∈[−1,0)∪(1,2]).