Article Search
eISSN 0454-8124
pISSN 1225-6951

### Article

Kyungpook Mathematical Journal 2020; 60(3): 467-475

Published online September 30, 2020

### On Diameter, Cyclomatic Number and Inverse Degree of Chemical Graphs

Reza Sharafdini*, Ali Ghalavand and Ali Reza Ashrafi

Department of Mathematics, Faculty of Science, Persian Gulf University, Bushehr 75169-13817, Iran
e-mail : sharafdini@pgu.ac.ir
Department of Pure Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan 87317-53153, Iran
e-mail : alighalavand@grad.kashanu.ac.ir and ashrafi@kashanu.ac.ir

Received: June 20, 2019; Revised: April 21, 2020; Accepted: April 22, 2020

### Abstract

Let G be a chemical graph with vertex set {v1, v1, … , vn} and degree sequence d(G) = (degG(v1), degG(v2), … , degG(vn)). The inverse degree, R(G) of G is defined as $R(G)=∑i=1n1degG(vi)$. The cyclomatic number of G is defined as γ = mn + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.

Keywords: diameter, cyclomatic number, pendant vertex, inverse degree, chemical graph