BICYCLIC GRAPHS WITH MINIMUM AND MAXIMUM FORGOTTEN AND INVERSE DEGREE INDICES

Subject Areas : Algebraic Structures and Optimization

mohammad ali manian ¹ , Shahram Heidarian ² , ّFarhad Khaksar Haghani ³

1 - Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
2 - Department of Mathematics, Shahrekord Branch, Islamic Azad University,Shahrekord, Iran
3 - Member of the faculty of Shahrekord Azad University

Received: 2024-03-03 Accepted : 2024-06-09 Published : 2024-06-17

Keywords: graph transformations, bicyclic graphs, forgotten index , inverse degree index,

Abstract :

In chemical graph theory, the forgotten index and inverse degree index of a connected simple graph G are defined as F(G) = ∑ 〖d_u^2+d_v^2 〗and ID(G) = ∑1/d_u respectively, where d_u represents the degree of vertex u in G. In this paper, we use some graph transformations and determine the minimum and the maximum values of the forgotten index and the inverse degree index on the class of bicyclic graphs. In addition, we characterize their corresponding extremal graphs.

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