Optimal Layout of (Kp − Cp)n into Wheel-Like Networks

Abstract

The problem of finding the induced subgraph with the maximum number of edges among all subsets of a fixed cardinality is known as the maximum subgraph problem (MSP). The lexicographic order has been proven optimal for Cartesian products of specific regular graphs [B. Sergei, B. Pavle and K. Nikola, New infinite family of regular edge isoperimetric graphs, Theoretical Computer Science 721 (2018) 42–53]. This paper is dedicated to the precise calculation of edge values within the resulting subgraphs, enhancing our comprehension of their structural properties and implications. In this paper, we focus on solving the MSP of [Formula: see text] for any [Formula: see text] and for odd [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] is obtained by the Cartesian product of a complete graph with [Formula: see text] vertices with a removal of a cycle on [Formula: see text] vertices. It has been observed that the graph obtained by deleting a cycle of length [Formula: see text] from a complete graph [Formula: see text] is isomorphic to a circulant graph [Formula: see text], while the particular case [Formula: see text] has been previously studied in [A. Syeda and M. Rajesh, MinLA of [Formula: see text] and its optimal layout into certain trees, The Journal of Supercomputing (2023), https://doi.org/10.1007/s11227-023-05140-3]. Our work extends the understanding of the MSP to a broader class of graphs with similar properties and applications.