R. B. Bapat 2 A. K. Lal3 Sukanta Pati 4 Abstract We consider a q-analogue of the distance matrix (called the q-distance matrix) of an unweighted tree and give formulae for the inverse and the determinant, which generalize the existing formulae for the distance matrix. We obtain the Smith normal form of the q-distance matrix of a tree. The relationship of the q-distance matrix with the Laplacian...

A strongly connected digraph is called a cactoid-type if each of its blocks consisting finitely many oriented cycles sharing common directed path. In this article, we find...

Given a graph $G$, the exponential distance matrix is defined entry-wise by letting $(u,v)$-entry be $q^{\text{dist}(u,v)}$, where $\text{dist}(u,v)$ between vertices $u$ and $v$ with convention that if are in different components, then $q^{\text{dist}(u,v)}=0$. In this paper, we will establish several properties of characteristic polynomial (spectrum) for matrix, give some families graphs whic...

The Mahalanobis Taguchi System (MTS) is a diagnosis and forecasting method for multivariate data. Mahalanobis distance (MD) is a measure based on correlations between the variables and different patterns that can be identified and analyzed with respect to a base or reference group. MTS is of interest because of its reported accuracy in forecasting small, correlated data sets. This is the type o...