On zeroth-order general Randić index of quasi-tree graphs containing cycles

  • Authors:

  • Shengning Qiao

  • Affiliations:

  • Department of Mathematics, Xidian University, Xi'an, Shaanxi 710071, PR China

  • Venue:
  • Discrete Optimization
  • Year:
  • 2010

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Abstract

Let G be a simple graph with the vertex set V(G) and @a be a real number with @a0. The zeroth-order general Randic index of G is defined as R"@a^0(G)=@?"v"@?"V"("G")d^@a(v), where d(v) denotes the degree of the vertex v in G. A graph G is called a quasi-tree graph, if there exists a vertex u@?V(G) such that G[V(G)@?{u}] is a tree. In this paper, we characterize the extremal quasi-tree graphs containing cycles with the minimum and maximum values of the zeroth-order general Randic index for @a in different intervals.