Counterexamples to a Conjecture on Wiener Index of Common Neighborhood Graphs
Counterexamples to a Conjecture on Wiener Index of Common Neighborhood Graphs
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发表时间：
2014
影响因子：
2.6
通讯作者：
C. Fonseca;M. Ghebleh;A. Kanso;D. Stevanović
中科院分区：
文献类型：
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作者：
C. Fonseca;M. Ghebleh;A. Kanso;D. Stevanović
对于简单图G，共同邻域图con(G)是与G具有相同顶点集的图，如果两个顶点在G中有共同邻域，则它们在con(G)中相邻。我们在这里描述了Knor等人的一个猜想的反例构造。数学。第一版。Chem. 72(2014)， 000-000]存在一个绝对常数C，使得对于每一个图G， W (con(G))≤C·W (G)，其中W (G)表示G的Wiener指数。
For a simple graph G, the common neighborhood graph con(G) is the graph with the same vertex set as G, with two vertices adjacent in con(G) if they have a common neighbor in G. We describe here constructions of counterexamples to a conjecture of Knor et al. [MATCH Commun. Math. Comput. Chem. 72 (2014), 000–000] that there exists an absolute constant C such that for every graph G it holds that W (con(G)) ≤ C ·W (G), where W (G) denotes the Wiener index of G.