A novel method to construct NSSD molecular graphs

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.

Nilpotent groups whose Difference graphs have positive genus

“…There are number of graphs attached to groups, in particular: Cayley graphs, commuting graphs, power graphs, enhanced power graph etc. These graphs have been studied extensively by various researchers because of their vast applications (see [16,19,20,22]). The power graph P(G) of a finite group G is a simple undirected graph with vertex set G such that two vertices a and b are adjacent if one is a power of the other.…”

Enumerating Tree-Like Graphs and Polymer Topologies with a Given Cycle Rank

“…Examples of a rooted graph H ∈ H (11,3), an ordered graph K = (H, π) of H with a left-to-right ordering π, and vertices indexed in SDFS ordering and canonical representation SR(K) of K are illustrated in Figure 4a-c.…”

“…The problem of enumerating discrete structures has several applications in applied fields such as graph theory, chemoinformatics, bioinformatics, and material informatics [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 ]. In particular, the enumeration of chemical compounds is widely used in the discovery of novel drugs [ 12 , 13 , 14 , 15 , 16 , 17 ] and structural elucidation [ 18 ].…”