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Mehdi Sohrabi haghighat

Mehdi Sohrabi haghighat

Academic rank: Assistant Professor
ORCID: https://orcid.org/0000-0001-5430-9159
Education: PhD.
ScopusId: 57074880700
Faculty: Science
Address: Arak University
Phone:

Research

Title
The minimum value of geometric-arithmetic index of graphs with minimum degree 2
Type
JournalPaper
Keywords
Geometric-arithmetic index, Extremal graphs, Linear programming
Year
2016
Journal J COMB OPTIM
DOI
Researchers Mohammadreza Rostami ، Mehdi Sohrabi haghighat

Abstract

The geometric-arithmetic index was introduced in the chemical graph theory and it has shown to be applicable. The aim of this paper is to obtain the extremal graphs with respect to the geometric-arithmetic index among all graphs with minimum degree 2. Let G(2, n) be the set of connected simple graphs on n vertices with minimum degree 2. We use linear programming formulation and prove that the minimum value of the first geometric-arithmetic (GA1)(GA1) index of G(2, n) is obtained by the following formula: GA∗1=⎧⎩⎨⎪⎪⎪⎪n24.794(n−2)2(n−2)√nn≤24,n=25,n≥26.