let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...

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let g be a simple connected graph and {v1, v2, …, vk} be the set of pendent (vertices ofdegree one) vertices of g. the reduced distance matrix of g is a square matrix whose (i,j)–entry is the topological distance between vi and vj of g. in this paper, we obtain the spectrumof the reduced distance matrix of thorn graph of g, a graph which obtained by attaching somenew vertices to pendent vertice...

Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

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