Naslov
A Note on the Maximum Value of W(L(G))/W(G)

Autori
Sedlar, Jelena ; Škrekovski, Riste

Izvornik
MATCH Communications in Mathematical and in Computer Chemistry (0340-6253) 88 (2022), 1; 171-178

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Wiener index ; Line graph

Sažetak
The line graph L(G) of a graph G is defined as a graph having vertex set identical with the set of edges of G and two vertices of L(G) are adjacent if and only if the corresponding edges are incident in G. Higher iteration Li(G) is obtained by repeatedly applying the line graph operation i times. Wiener index W(G) of a graph G is defined as the sum of distances which runs over all pairs of vertices in G. The problem of establishing the extremal values and extremal graphs for the ratio W(Li(G))/W(G) was proposed by Dobrynin and Melnikov [Mathematical Chemistry Monographs, Vol. 12, 2012, pp. 85-121]. In this paper we establish the maximum value and characterize the extremal graphs for i=1. In doing so, we derive unexpectedly an interesting relation that involves the Gutman index and the first Zagreb index.

Izvorni jezik
Engleski

POVEZANOST RADA