eccentric adjacency index
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2018 ◽  
Vol 13 (01) ◽  
pp. 2050028 ◽  
Author(s):  
Shehnaz Akhter ◽  
Rashid Farooq

Let [Formula: see text] be a simple connected graph with vertex set [Formula: see text] and edge set [Formula: see text]. The eccentricity [Formula: see text] of a vertex [Formula: see text] in [Formula: see text] is the largest distance between [Formula: see text] and any other vertex of [Formula: see text]. The eccentric adjacency index (also known as Ediz eccentric connectivity index) of [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the sum of degrees of neighbors of the vertex [Formula: see text]. In this paper, we determine the unicyclic graphs with largest eccentric adjacency index among all [Formula: see text]-vertex unicyclic graphs with a given girth. In addition, we find the tree with largest eccentric adjacency index among all the [Formula: see text]-vertex trees with a fixed diameter.


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