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Abstract
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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.
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