Abstract
Topological indices and polynomials are predicting properties like boiling points, fracture toughness, heat of formation, etc., of different materials, and thus save us from extra experimental burden. In this article we compute many topological indices for the family of circulant graphs. At first, we give a general closed form of M-polynomial of this family and recover many degree-based topological indices out of it. We also compute Zagreb indices and Zagreb polynomials of this family. Our results extend many existing results.
Highlights
A number, polynomial or a matrix can uniquely identify a graph
A topological index is a numeric number associated to a graph which completely describes the topology of the graph, and this quantity is invariant under the isomorphism of graphs
The degree-based topological indices are derived from degrees of vertices in the graph
Summary
A number, polynomial or a matrix can uniquely identify a graph. A topological index is a numeric number associated to a graph which completely describes the topology of the graph, and this quantity is invariant under the isomorphism of graphs. The degree-based topological indices are derived from degrees of vertices in the graph. These indices have many correlations to chemical properties. The study of topological indices, based on distance in a graph, was effectively employed in 1947 in chemistry by Weiner [1]. Polynomial ( called the Wiener polynomial) [9] It plays a vital role in determining distance-based topological indices. The M-polynomial—introduced recently in 2015 [10]—plays the same role in determining the closed form of many degree-based topological indices. For a simple connected graph, the first Zagreb polynomial is defined as: Where Dx ( f ( x, y)) = x. Multi-level and antipodal labelings for circulant graphs is discussed in [29,30]
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