On the General Eccentric Connectivity Coindex of Graphs
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Date
2024-08
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Addis Ababa University
Abstract
In this thesis, we introduce the general eccentric connectivity coindex, ECCIa of connected
graphs. For a connected graph G order n, we define the general eccentric connectivity coindex
as
ECCIa(G) = Σ
v∈V(G)
ecca
G[n−1−dG(v)]
for a ∈ R, where E(G) is the edge set of graph G , dG(v) is the degree of vertex v and V(G)
is the vertex set of graph G.
We study, the general eccentric connectivity coindex of tree graphs of a given graph
parameters. We determine trees with the maximum and minimum general eccentric connectivity
coindex among all trees of a given graph parameters for a > 1.
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Keywords
General Eccentric, Connectivity Coindex, Graphs