"Extremal graphs and bounds for general Gutman index" by Swathi Shetty, B. R. Rakshith et al.
 

Extremal graphs and bounds for general Gutman index

Document Type

Article

Publication Title

AIMS Mathematics

Abstract

For a connected graph G, the general Gutman index was denoted by Guta,b (G) and was ∑ given by Guta,b (G) = [dG (u)dG (v)]a [dG (u, v)]b, where a, b ∈ R, dG (x) was the degree of vertex {u,v}⊆V(G) x in G and dG (u, v) denoted the distance between vertices u and v in G. In this paper, we solved some open problems on general Gutman index. More precisely, we characterized unicyclic graphs with extremal general Gutman index for some a and b. We presented a sharp bound on general Gutman index of G in terms of order and vertex connectivity of G. Also, we obtained some bounds on general Gutman index in terms of order, general Randić index, diameter, and independence number of graph G. In addition, QSPR analysis on various anticancer drug structures was carried out to relate their physicochemical properties with the general Gutman index of the structure for some a and b.

First Page

30454

Last Page

30471

DOI

10.3934/math.20241470

Publication Date

1-1-2024

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