C = network connectivity C = total journey cost D = matrix of maximum communication range between nodes (Rn×n) E = set of edges in G EG = subset of edges in G G = graph containing all nodes and edges G = evolving graph H = number of hops in a journey J = set of feasible journeys J = journey between nodes J = highest-value journey M = total number of edges in G m = number of edges in G N = total...

Let Mn,m be the set of all n × m matrices with entries in F, where F is the field of real or complex numbers. A matrix R ∈ Mn with the property Re=e, is said to be a g-row stochastic (generalized row stochastic) matrix. Let A,B∈ Mn,m, so B is said to be gw-majorized by A if there exists an n×n g-row stochastic matrix R such that B=RA. In this paper we characterize all linear operators that stro...

In the present paper, we give upper and lower bounds for the spectral norm of g-circulant matrix, whose the rst row entries are the classical Horadam numbers U (a,b) i . In addition, we also establish an explicit formula of the spectral norm for g-circulant matrix with the rst row ([U (a,b) 0 ] , [U (a,b) 1 ] , · · · , [U (a,b) n−1 ]).

We show that a cubic graph G with girth g(G) ≥ 5 has a Hamiltonian Circuit if and only if the matrix A+ I can be row permuted such that each column has at most 2 blocks of consecutive 1’s, where A is the adjacency matrix of G, I is the unit matrix, and a block can be consecutive in circular sense, i.e., the first row and the last row are viewed as adjacent rows. Then, based on this necessary an...

We construct Cheeger-type bounds for the second eigenvalue of a substochastic transition probability matrix in terms of the Markov chain’s conductance and metastability (and vice-versa) with respect to its quasi-stationary distribution, extending classical results for stochastic transition matrices.

In this paper, we consider a g-circulant matrixA 1(T), whose the first row entries are generalized Tribonacci numbers T(a)i. We give an explicit formula of spectral norm matrix. When g = 1, also present upper and lower bounds for spread 1-circulant matrix A1(T).

A long line of research on fixed parameter tractability integer programming culminated with showing that programs $n$ variables and a constraint matrix dual tree-depth $d$ largest entry $\Delta$ are solvable in time $g(d,\Delta){poly}(n)$ for some function $g$. However, the is not preserved by row operations, i.e., given program can be equivalent to another smaller tree-depth, thus does reflect...

Given a Graph G = ((V(G),E(G)), and a subset ) (G V S  , S with a given property(covering set, Dominating set, Neighbourhood set), we define a matrix taking a row for each of the minimal set corresponding to the given property and a column for each of the vertex of G. The elements of the matrix are 1 or 0 respectively as the vertex is contained in minimal set or otherwise. That is matrix (mij)...

Heyman gives an interesting factorization of I ? P , where P is the transition probability matrix for an ergodic Markov Chain. We show that this factoriza-tion is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to...