Some Invariants of Circulant Graphs

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.

M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes

“…Recently, Munir et al computed M-polynomials and related topological indices for Nanostar dendrimers [15], titania nanotubes [16], and circulant graphs [17]. The structures of Nanostar dendrimers and titania nanotubes are different from polyhex nanotubes from a geometrical point of view.…”

Some Computational Aspects of Boron Triangular Nanotubes

“…Algebraic polynomials have also useful applications in chemistry, such as Hosoya polynomial (also called Wiener polynomial) [8], which plays a vital role in determining distance-based topological indices. Among other algebraic polynomials, the M-polynomial [9], introduced in 2015, plays the same role in determining the closed form of many degree-based topological indices [10][11][12][13][14]. The main advantage of M-polynomial is the wealth of information that it contains about degree-based graph invariants.…”

K Banhatti and K hyper Banhatti indices of circulant graphs

“…Classes of graphs that are circulant include the, antiprism graphs, crown graphs, cocktail party graphs, rook graphs, complete bipartite graphs, Andrásfai graphs, empty graphs, complete graphs, Paley graphs of prime order, Möbius ladders, torus grid graphs, and prism graphs. Because of this somewhat universality, circulant graphs have been the subject of much investigation; for example, the chromatic index, Connectivity, Wiener index, domination number, revised Szeged spectrum, Multi-level and antipodal labeling, M polynomial and many degree-based topological indices for circulant graphs are studied (Voigt and Walther, 1991;Boesch, and Tindell, 1984;Zhou, 2014;Xueliang et al, 2011;Habibi and Ashrafi, 2014;Kang et al, 2016;Nazeer et al, 2015;Munir et al, 2016). For details on topological indices readers are refered to Sardar et al (2017) and Rehman et al (2017).…”