A matrix method for computing Szeged and vertex PI indices of join and composition of graphs

The Szeged index extends the Wiener index for cyclic graphs by counting the number of vertices on both sides of each edge and sum these counts. Klavzar et al. [S. Klavzar, A. Rajapakse, I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett. 9 (5) (1996) 45–49] provided an exact form...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 429; no. 11; pp. 2702 - 2709
Main Authors Khalifeh, M.H., Yousefi-Azari, H., Ashrafi, A.R.
Format Journal Article Conference Proceeding
LanguageEnglish
Published New York, NY Elsevier Inc 01.12.2008
Elsevier Science
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Summary:The Szeged index extends the Wiener index for cyclic graphs by counting the number of vertices on both sides of each edge and sum these counts. Klavzar et al. [S. Klavzar, A. Rajapakse, I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett. 9 (5) (1996) 45–49] provided an exact formula for computing Szeged index of product of graphs. In this paper, we apply a matrix method to obtain exact formulae for computing the Szeged index of join and composition of graphs. The join and composition of the vertex PI index of graphs are also computed.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2008.01.015