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 - Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran

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

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

Abstract :

For a connected simple graph G, the inverse degree index and forgotten index are defined as F(G) = P uv∈E(G) [d 2 u + d 2 v ] and ID(G) = P u∈V (G) 1 du respectively, where du represents the degree of vertex u in G. In this paper, we use some graph transformations and determine the minimum and maximum values of forgotten index and inverse degree index on the class of bicyclic graphs and characterize their corresponding extremal graphs.

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