Sharp Lower Bound of Cacti Graph with respect to Zagreb Eccentricity Indices

Abstract

The first Zagreb eccentricity index E1℧ is the sum of square of eccentricities of the vertices, and the second Zagreb eccentricity index E2℧ is the sum of product squares of the eccentricities of the vertices. A linked graph G is called a cactus if any two of its cycles share only one vertex. In other words, there are no two independent cycles that share an edge. Cactus graphs are also known as “block graphs” or “sensitized graphs.” They are closely related to chordal graphs and can be used to represent various types of networks, including communication networks and road networks. In this contribution, E1℧ and E2℧ values of cacti with k pendant vertices and k cycles, respectively, are considered. We determine the minimum E1,E2 indices for n order cacti with k pendant vertices and k cycles.