Reza Sharafdini

The eccentric adjacency index (for short, EAI) of a connected graph G is defined as ξad(G) = ∑ u∈V(G) SG(u)εG(u)−1, where SG(u) denotes sum of degrees of vertices adjacent to the vertex u and εG(u) is defined as the maximum length of any minimal path connecting u to any other vertex of G. Inspired from [Jelena Sedlar, On augmented eccentric connectivity index of graphs and trees, MATCH Commun. Math. Comput. Chem. 68 (2012) 325–342.], we establish all extremal graphs with respect to EAI among all (simple connected) graphs, among trees and among trees with perfect matching.