On Extremal Values Of Total Structure Connectivity and Narumi-Katayama Indices on the Class of all Unicyclic and Bicyclic Graphs
نویسندگان
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
doi
10.22052/ijmc.2023.252930.1716چکیده
The total structure connectivity and Narumi-Katayama indices of a simple graph $G$ are defined as $TS(G)={\prod_{{u}\in{V(G)}}}{\frac{1}{\sqrt {{d_{u}}}}}$ and $ NK(G)={\prod_{{u}\in{V(G)}}{{d_{u}}}}$ respectively, where $d _{u} $ represents the degree of vertex $ u $ in $ G $. In this paper, we determine the extremal values of total structure connectivity index on the class of unicyclic and bicyclic graphs and characterize the corresponding extremal graphs. In addition, we determine the bicyclic graphs extremal with respect to the Narumi-Katayama index.
