Abstract: Recent developments in the storage of system data in the Navy's data repository, LEAPS, using the FOCUS product meta-model have opened the doors to graph-theory applications in the design of ...

Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

The metric dimension is a key invariant in graph theory that encapsulates the minimal number of reference points, or “resolving sets”, required to uniquely determine the position of each vertex within ...

ABSTRACT: For a simple undirected graph G, let A( G ) be the (0, 1) adjacency matrix of G. The Seidel matrix of G, is defined as S( G )=J−I−2A( G ) , where J is the all-one matrix and I is the ...