A new M-matrix of Type III, its properties and applications

TL;DR

This paper introduces a new class of M-matrices of Type III, explores their mathematical properties, and demonstrates their applications in combinatorial design theory and graph construction.

Contribution

It presents the first detailed study of M-matrices of Type III, including their properties and applications, extending previous work on Type I and II matrices.

Findings

Constructed new M-matrices of Type III

Developed methods for creating SPBIB designs

Linked M-matrices to M-graph constructions

Abstract

Some binary matrices like (1,-1) and (1,0) were studied by many authors like Cohn, Wang, Ehlich and Ehlich and Zeller, and Mohan, Kageyama, Lee, and Gao. In this recent paper by Mohan et al considered the M-matrices of Type I and II by studying some of their properties and applications. In the present paper they discussed the M-matrices of Type III, and studied their properties and applications. They gave some constructions of SPBIB designs and some corresponding M-graphs, which are being constructed by it. This is the continuation of our earlier research work in this direction, and these papers establish the importance of non-orthogonal matrices as well.