On the General Eccentric Connectivity Index of Graphs
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Date
2024-08
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Addis Ababa University
Abstract
The general eccentric connectivity index of graphs is the main topic of this study. For a connected graph G, the general eccentric connectivity index of graph G is defined by ECIa(G) = Σ
v∈V(G)
eccG(v)daG
(v)
for a ∈ R, where the degree of v in G is dG(v), the eccentricity of vertex v is eccG(v), and the
vertex set of G is V(G).
In this thesis, we study the general degree-eccentricity index of graphs. Among all the unicyclic graphs of a particular order and matching number, we identify the unicyclic graphs with the largest and smallest general eccentric connectivity index.
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Keywords
General Eccentric, Connectivity Index, Graphs