Wiener index of strong product of graphs | Zendy

Iztok Peterin | Zendy; Petra Žigert Pleteršek | Zendy

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Wiener index of strong product of graphs

Author(s) -

Iztok Peterin,

Petra Žigert Pleteršek

Publication year - 2017

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2018.38.1.81

Subject(s) - wiener index , mathematics , combinatorics , graph , product (mathematics) , constant (computer programming) , connectivity , topological index , index (typography) , discrete mathematics , geometry , computer science , world wide web , programming language

The Wiener index of a connected graph ▫$G$▫ is the sum of distances between all pairs of vertices of ▫$G$▫. The strong product is one of the four most investigated graph products. In this paper the general formula for the Wiener index of the strong product of connected graphs is given. The formula can be simplified if both factors are graphs with the constant eccentricity. Consequently, closed formulas for the Wiener index of the strong product of a connected graph ▫$G$▫ with a cycle are derived.Wienerjev indeks povezanega grafa ▫$G$▫ je vsota razdalj med vsemi pari vozlišč grafa ▫$G$▫. Krepki produkt spada med štiri najbolj raziskovane grafovske produkte. V tem delu predstavimo splošno formulo za Wienerjev indeks krepkega produkta povezanih grafov. Če imata oba grafa konstantno ekscentričnost, se formula poenostavi. Posledica tega so zaprte formule za Wienerjev indeks krepkega produkta povezanega grafa ▫$G$▫ s ciklom, ki so tudi predstavljene

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