A Study on Emergence of Clutch Graphs from Cycle Graphs: A Comprehensive Analysis

Abstract

The clutch is one of the substantial devices for constructing vehicles in automobile engineering. In terms of network toughness against failures or disruptions, the clutch-based graph can be used to model insufficiency of primary pathways and the availability of alternative routes in communication networks. In this paper, the identification of the clutch graph Cl3n(G) from the cycle graph Cn(G) has been proposed. A clutch graph Cl3n(G) generating from a cycle graph with 3n vertices and 4n edges (n ≥ 4 and even). The notions of degree, girth, and chromatic number of the clutch graph have been discussed. Further, the existence of the bipartite and Hamiltonian graphs on the clutch graph has been examined.