DETERMINANT OF ANTICHAIN GRAPHS

Networks, in the form of bipartite graphs, are abundant in existence. A network having no redundant connections has proved to be more efficient and cost-effective too. Antichain graphs are a class of bipartite graphs having no redundant connections. Matrices provide models for graphs that illuminate their structure. The determinant is one of the powerful linear algebraic tools, that has been used extensively to study graphs. In this article, two of the powerful linear algebraic parameters namely, the determinant and permanent of adjacency matrix of antichain graphs are studied. This article characterizes the antichain graphs with nonzero determinants, which in turn, are the graphs with positive nullity.