On the structure and edge multiplicity of cospectral k - crowded chordal networks

Abstract

The study of connectivity has become increasingly significant as networks find application in numerous domains. Our objective was to discern characterization of chordal communities(or sub networks) within a network or the cospectral chordal network of k-crowded chordal communities. The multiplicity of edges AB in G is presented by $me_G(AB) = |Ng_G(A) \cap Ng_G(B)|$. A k-crowded chordal community of cospectral chordal network G, referred to as $CCC_k(G)$ is maximally linked sub network formed by the vertex set for an integer k, where $k \geq 4$ i.e.,\\

$$V_{CCC_k}(G) = \{A \in V(G), B \in V(G)$$ such that $\; AB \in E(G)$ \; and $\; me_{CCC_k}(G)(AB) \geq k - 4\}$

This research pinpoint networks that are k-crowded yet not (k+1)-crowded for certain values of k. It furthermore investigates the least and greatest number of edges present in these networks. Grasping k-crowded chordal sub networks, which are referred to as communities can help in analyzing connectedness, practical instances consist of large, intricate networks (or graphs).