Let G = (V, E) be a graph with V = {1, 2, . . . , n}, in which we allow parallel edges but no loops, and let S+(G) be the set of all positive semi-definite n × n matrices A = [ai,j ] with ai,j = 0 if i = j and i and j are non-adjacent, ai,j = 0 if i = j and i and j are connected by exactly one edge, and ai,j ∈ R if i = j or i and j are connected by parallel edges. The maximum positive semi-defi...

INTRODUCTION Section 5(ii) of The Hindu Marriage Act, 1955 (HMA) states that under certain circumstances, mental illness is accepted as a ground for the annulment of marriage, while Section 13(1) (iii) states that mental illness is a ground for divorce. There is little data on how this provision is used and applied in matrimonial petitions. This paper assesses judicial practices in divorce case...

Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n+, n−, n0) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n0 denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n− 2ν(G). Gu...

It is shown that if G is a graph with an odd number of spanning trees, then the line graph L(G) of G has nullity at most one.

A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH(G), is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH(G), which combines the cases of undirected and oriented unicyclic ...