Circulants and their connectivities

Abstract

There is diverse literature on various properties of a class of graphs known as circulants. We present a new result which answers the previously unsolved question of characterizing the connection sequence of circulants having point connectivity equal to point degree. We also develop some theorems regarding a new generalization of connectivity known as superconnectivity. In addition, we give a survey of ,published results pertinent to the study of connectivity of circulants.

Further Topics in Connectivity

“…In this context, other good topologies are provided by Cayley graphs of Abelian groups, also called loop networks (see [BeCoHs95], [BoTi84]). …”

“…The case S 0 = S in Fact F88 (that is, for circulant graphs) was proved in [BoFe70] using the "convexity conditions" b i+1 b i b i b i 1 (see also [BoTi84]). …”

The Symmetric Circulant Traveling Salesman Problem

“…A well known theorem due to Boesch, and Tindell (1984), and concerning the connectivity of a circulant weighted undirected graph can be restated for G  (α D ) as follows. Gilmore, et al (1985)).…”

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).…”