Bicyclic graphs with minimum and maximum forgotten and inverse degree indices
محورهای موضوعی : ساختارهای جبری و بهینه سازیMohammad 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
کلید واژه: graph transformations, bicyclic graphs, forgotten index, inverse degree index,
چکیده مقاله :
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.
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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