2013/11/28 by J. A. Rodríguez, J. M. Sigarreta
Mathematics · #math.CO
published as MATCH Communications in Mathematical and in Computer Chemistry 54 (2) (2005) 403-416 · arXiv admin note: text overlap with arXiv:math/0602437
arxiv created 2013/11/28 · arxiv updated 2013/12/02
The aim of this paper is to study some parameters of simple graphs related with the degree of the vertices. So, our main tool is the n× n matrix \cal A whose (i,j)-entry is aij= \lbrace (1)/(√(δiδj)) · \rm if vi∼ vj ;
0 · \rm otherwise, . where δi denotes the degree of the vertex vi. We study the Randić index and some interesting particular cases of conditional excess, conditional Wiener index, and conditional diameter. In particular, using the matrix \cal A or its eigenvalues, we obtain tight bounds on the studied parameters.