\(D\)-Graphs for Graphs with Cyclomatic Number \(1\)

Edward J.Farrell1, Andrew A.Hunte1
1The Centre for Graph Polynomials Department of Mathematics and Statistics The University of the West Indies St. Augustine, Trinidad

Abstract

We identify a graph without proper cycles, which is comatching with a cycle,The result is then extended to certain general families of graphs with cyclomatic number \(1\), formed by attaching trees to cycles.