A Novel Method to Construct NSSD Molecular Graphs

TL;DR

This paper introduces a new method for constructing NSSD molecular graphs using commuting graphs of the H_v-group, which is significant for understanding the conductance in organic chemistry.

Contribution

It presents a novel algorithm for building NSSD graphs from the commuting graphs of the H_v-group, advancing graph construction techniques in chemical graph theory.

Findings

Successfully constructs NSSD graphs from H_v-group commuting graphs

Provides an algorithm for NSSD graph construction

Enhances understanding of molecular conductance models

Abstract

A graph is said to be NSSD (= non-singular with a singular deck) if it has no eigenvalue equal to zero, whereas all its vertex-deleted subgraphs have eigenvalues equal to zero. NSSD graphs are of importance in the theory of conductance of organic compounds. In this paper, a novel method is described for constructing NSSD molecular graphs from the commuting graphs of the $H_v$-group. An algorithm is presented to construct the NSSD graphs from these commuting graphs.