Abstract
Topological index is an invariant of molecular graphs which correlates the structure with different physical and chemical invariants of the compound like boiling point, chemical reactivity, stability, Kovat’s constant etc. Eccentricity-based topological indices, like eccentric connectivity index, connective eccentric index, first Zagreb eccentricity index, and second Zagreb eccentricity index were analyzed and computed for families of Dutch windmill graphs and circulant graphs.
Highlights
A single number which represents a chemical structure, in graph-theoretical chemistry, is called a topological descriptor
Topological indices are mainly used in quantitative structure–activity relations (QSAR) as well as quantitative structure–property relations (QSPR) which describe the relation between chemical structure with the properties and reactivity of the compounds
Dutch Windmill graph: A graph Dm m common vertex is known as Dutch windmill graph
Summary
A single number which represents a chemical structure, in graph-theoretical chemistry, is called a topological descriptor (or index). Let u ∈ V be the eccentricity of a vertex where u is a maximum distance of u from other vertices of graph G, which is denoted by ε(u), i.e., ε(u) = max{d(u, v); v ∈ V }, where d(u, v) is a distance between u and v. The connective eccentricity index of Dutch windmill graph, denoted by C ξ I f m is even n be the Dutch windmill graph with n copies of cycle C having common vertex z with Proof.
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