- Tytuł:
- Wiener and vertex PI indices of the strong product of graphs
- Autorzy:
-
Pattabiraman, K.
Paulraja, P. - Powiązania:
- https://bibliotekanauki.pl/articles/743324.pdf
- Data publikacji:
- 2012
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
strong product
Wiener index
hyper-Wiener index
vertex PI index - Opis:
- 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2012, 32, 4; 749-769
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł