Extremal conjugated unicyclic and bicyclic graphs with respect to total-eccentricity index

Abstract

Let $G$ be a molecular graph. The total-eccentricity index of graph $G$ is defined as the sum of eccentricities of all vertices of $G$. %In [R. Farooq, M.A. Malik, J. Rada, Extremal graphs with respect to total-eccentricity index, 2017, submitted], the authors studied The extremal trees, unicyclic and bicyclic graphs, and extremal conjugated trees with respect to total-eccentricity index are known. In this paper, we extend these results and study the extremal conjugated unicyclic and bicyclic graphs with respect to total-eccentricity index.