A new class of simple symmetric digraphs called D is defined and studied here. Any digraph in D has the property that each non-pendant is adjacent to at least one pendant vertex. A graph theoretical description for the ...

In this article, we characterize Cohen-Macaulay permutation graphs. In particular, we show that a permutation graph is Cohen-Macaulay if and only if it is well-covered and there exists a unique way of partitioning its ...

Graham showed with Pollak and Hoffman-Hosoya that for any directed graph G with strong blocks Ge, the determinant det(DG) and cofactor-sum cof(DG) of the distance matrix DG can be computed from the same quantities for the ...

The quadratic embedding constant (QEC) of a finite, simple, connected graph G is the maximum of the quadratic form of the distance matrix of G on the subset of the unit sphere orthogonal to the all-ones vector. The study ...

Generalized digamma functions ψk(x), studied by Ramanujan, Deninger, Dilcher, Kanemitsu, Ishibashi etc., appear as the Laurent series coefficients of the zeta function associated to an indefinite quadratic form. In this ...

In this paper we propose a generalization of the Grothendieck inequality for pairs of Banach spaces E and F with E being finite dimensional and investigate the behaviour of the Grothendieck constant KG(E,F) implicit in ...

In this paper, we study the class of affine semigroup generated by integral vectors, whose components are in generalised arithmetic progression and we observe that the defining ideal is determinantal. We also give a ...

In this semi-expository short note, we prove that the only homogeneous \textit{pure} hyponormal operator T with rank(T∗T−TT∗)=1, modulo unitary equivalence, is the unilateral shift.

Let (G,w) be an undirected weighted graph. The group inverse of (G,w) is the weighted graph with the adjacency matrix A#, where A is the adjacency matrix of (G,w). We study the group inverse of singular weighted trees. It ...

We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad equations:(|Du|γM+λ,ΛD2u(x) = f|u ≥ u(x)| in Ωu = g on ∂,where γ≥1 is a constant, Ω is a bounded domain in RN with C1,1 boundary. ...