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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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
Subjects
Algebra
Exact sciences and technology
Graph composition
Graph join
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Szeged index
Vertex PI index
Vertex PI index
Graph composition
Graph join
Szeged index
Cyclic
Matrix method
Vertex(graph)
Graph theory
Counting
Enumeration(counting)
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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