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2012 | 32 | 4 | 749-769
Tytuł artykułu

Wiener and vertex PI indices of the strong product of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Wiener index of a connected graph G, denoted by W(G), is defined as $½ ∑_{u,v ∈ V(G)}d_G(u,v)$. Similarly, the hyper-Wiener index of a connected graph G, denoted by WW(G), is defined as $½W(G) + ¼ ∑_{u,v ∈ V(G)} d²_G(u,v)$. The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, the exact formulae for Wiener, hyper-Wiener and vertex PI indices of the strong product $G ⊠ K_{m₀,m₁,...,m_{r -1}}$, where $K_{m₀,m₁,...,m_{r -1}}$ is the complete multipartite graph with partite sets of sizes $m₀,m₁, ...,m_{r -1}$, are obtained. Also lower bounds for Wiener and hyper-Wiener indices of strong product of graphs are established.
Wydawca
Rocznik
Tom
32
Numer
4
Strony
749-769
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-06-20
poprawiono
2012-01-25
zaakceptowano
2012-01-27
Twórcy
  • Department of Mathematics, Annamalai University, Annamalainagar 608 002, India
autor
  • Department of Mathematics, Annamalai University, Annamalainagar 608 002, India
Bibliografia
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  • [23] K. Pattabiraman and P. Paulraja, Vertex and edge Padmakar-Ivan indices of the generalized hierarchical product of graphs, Discrete Appl. Math. 160 (2012) 1376-1384, doi: 10.1016/j.dam.2012.01.021.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1647
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