let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

Hamiltonian Cycles in Directed Toeplitz Graphs Dr Shabnam Malik Faculty of Mathematics, Forman Christian College University, Lahore Pakistan An (n × n) matrix A = (aij) is called a Toeplitz matrix if it has constant values along all diagonals parallel to the main diagonal. A directed Toeplitz graph is a digraph with Toeplitz adjacency matrix. In this talk I will discuss conditions for the exist...

In this paper we will consider hamiltonian properties of so-called Toeplitz graphs, which are defined as follows: Definition 1 Let n,m, a1, . . . , am ∈ N, 0 < a1 < · · · < am < n and V := {0, . . . , n− 1}. Define E := {[i, j] ∈ V 2 : ∃k ∈ {1, . . . , m} : |j − i| = ak}. Then the graph (V,E) with set of vertices V and set of edges E is called an undirected Toeplitz graph with entries (or strip...

We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.

In this paper, we study structural properties of Toeplitz graphs. We characterize Kq-free graphs for an integer q≥3 and give equivalent conditions a graph Gn〈t1,t2,…,tk〉 with t1<⋯<tk n≥tk−1+tk being chordal Gn〈t1,t2〉 perfect. Then compute the edge clique cover number vertex graph. Finally, degree sequence (d1,d2,…,dn) n vertices show that is regular if only it circulant

The doubly resolving sets are a natural tool to identify where diffusion occurs in complicated network. Many real-world phenomena, such as rumour spreading on social networks, the spread of infectious diseases, and virus internet, may be modelled using information networks. It is obviously impractical monitor every node due cost overhead limits because there too many nodes network, some which u...

Cliques and odd cycles are well known to induce facet-de.ning inequalities for the stable set polytope. In graph coloring cliques are a class of n-critical graphs whereas odd cycles represent the class of 3-critical graphs. In the .rst part of this paper we generalize both notions to (Kn \ e)-cycles, a new class of n-critical graphs, and discuss some implications for the class of in.nite planar...

An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.