Title of article :
On Extremal Values Of Total Structure Connectivity and Narumi-Katayama Indices on the Class of all Unicyclic and Bicyclic Graphs
Author/Authors :
Manian ، Mohammad Ali Department of Mathematics - Islamic Azad University, Shahrekord Branch , Heidarian ، Shahram Department of Mathematics - Islamic Azad University, Shahrekord Branch , Khaksar Haghani ، Farhad Department of Mathematics - Islamic Azad University, Shahrekord Branch
Abstract :
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.
Keywords :
Graph transformations , Unicyclic graphs , Bicyclic graphs , Total structure connectivity index , Narumi , Katayama index
Journal title :
Iranian Journal of Mathematical Chemistry
Journal title :
Iranian Journal of Mathematical Chemistry
