The spectral radius p(A) of the adjacency matrix A of a graph G with e edges satisfiesp(A)<i(-l+~~).Equalityoccnrsifandonlyif e= i andGisa disjoint union of the complete graph K, and isolated vertices. 0 Let A be a symmetric (0,l) matrix with zero trace (i.e., the adjacency matrix of a graph G). Let the number of l’s of A be 2 (k) (so G has (i) edges). R. A. Brualdi and A. J. Hoffmann [l, Theor...

Let G be a strongly connected digraph, and dG(vi,vj) denote the distance from vertex vi to vj defined as length of shortest directed path in G. The sum between vertices is sdG(vi,vj)=dG(vi,vj)+dG(vj,vi). matrix n×n SD(G)=(sdG(vi,vj))vi,vj∈V(G). For vi∈V(G), transmission G, denoted by STG(vi) or STi, row SD(G) corresponding vi. ST(G)=diag(ST1,ST2,…,STn) diagonal with transmissions zeroes elsewhe...

Abstract We prove that for all $$n\in {\mathbb {N}}$$ n ∈ N , there exists a constant $$C_{n}$$ C such $$d \in d every row contraction T consisting of d commuting $$n \times n$$ ×...

In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The RandomnessImpreciseness Consistency Principle l...

A permuted graph matrix is a matrix V ∈ C(m+n)×m such that every row of the m×m identity matrix Im appears at least once as a row of V . Permuted graph matrices can be used in some contexts in place of orthogonal matrices, for instance when giving a basis for a subspace U ⊆ Cm+n, or to normalize matrix pencils in a suitable sense. In these applications the permuted graph matrix can be chosen wi...