Bicyclic Graphs with Minimum General Sum-connectivity Index
نویسندگان
چکیده
Du, Zhou and Trinajstić [J. Math. Chem., 48, pp. 697–703, 2010] proved that in the set of n-vertex connected unicyclic graphs G with n ≥ 3, for –1 ≤ α < 0, the graph consisting of a triangle and n – 3 pendant vertices adjacent to the same vertex of this triangle is the unique graph with the minimum general sum-connectivity index. In this paper, using a graph transformation and several inequalities, we show that in the class of n-vertex connected bicyclic graphs G with n ≥ 4, the graph consisting of two triangles having a common edge and n – 4 pendant vertices adjacent to the same vertex of degree three of this graph is the unique graph minimizing the general sum-connectivity index for –1 ≤ α < 0.
منابع مشابه
On Sum–Connectivity Index of Bicyclic Graphs
We determine the minimum sum–connectivity index of bicyclic graphs with n vertices and matching number m, where 2 ≤ m ≤ ⌊n2 ⌋, the minimum and the second minimum, as well as the maximum and the second maximum sum–connectivity indices of bicyclic graphs with n ≥ 5 vertices. The extremal graphs are characterized. MSC 2000: 05C90; 05C35; 05C07
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