Trees of extremal connectivity index

Authors:
Huiqing Liu;Mei Lu;Feng Tian
Affiliations:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China;Department of Mathematical Sciences, Tsinghua University, Beijing, China;Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

The connectivity index wα(G) of a graph G is the sum of the weights (d(u)d(v))α of all edges uv of G, where α is a real number (α ≠ 0), and d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k pendant vertices. In this paper, we give sharp lower and upper bounds for w1(T). Also, for - 1 ≤ α wα(T).