scholarly journals On Self-Centeredness of Product of Graphs

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Priyanka Singh ◽  
Pratima Panigrahi
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lexicographic Product ◽  
Normal Product ◽  
Strong Product ◽  
Necessary And Sufficient ◽  
Product Of Graphs

A graph G is said to be a self-centered graph if the eccentricity of every vertex of the graph is the same. In other words, a graph is a self-centered graph if radius and diameter of the graph are equal. In this paper, self-centeredness of strong product, co-normal product, and lexicographic product of graphs is studied in detail. The necessary and sufficient conditions for these products of graphs to be a self-centered graph are also discussed. The distance between any two vertices in the co-normal product of a finite number of graphs is also computed analytically.

On multilattice groups. II

1966 ◽  
Vol 62 (2) ◽  
pp. 149-164 ◽  
Author(s):  
D. B. Mcalister
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Positive Element ◽  
Necessary And Sufficient Conditions ◽  
Countable Number ◽  
Direct Sums ◽  
Lattice Group ◽  
Ordered Groups ◽  
Group A ◽  
Necessary And Sufficient

Conrad ((2)), has shown that any lattice group which obeys (C.F.) each strictly positive element exceeds at most a finite number of pairwise orthogonal elements may be constructed, from a family of simply ordered groups, by carrying out, alternately, the operations of forming finite direct sums and lexico extensions, at most a countable number of times. The main result of this paper, Theorem 3.1, gives necessary and sufficient conditions for a multilattice group, which obeys (ℋ*), to be isomorphic to a multilattice group which is constructed from a family of almost ordered groups, by carrying out, alternately, the operations of forming arbitrary direct sums and lexico extensions, any number of times; we call such a group a lexico sum of the almost ordered groups.

scholarly journals Pointwise stabilization of the Poisson integral for the diffusion type equations with inertia

2016 ◽  
Vol 8 (2) ◽  
pp. 279-283
Author(s):  
H.P. Malytska ◽  
I.V. Burtnyak
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Poisson Integral ◽  
Diffusion Type ◽  
Necessary And Sufficient ◽  
Parabolic Degeneracy

In this paper we consider the pointwise stabilization of the Poisson integral for the diffusion type equations with inertia in the case of finite number of parabolic degeneracy groups. We establish necessary and sufficient conditions of this stabilization for a class of bounded measurable initial functions.

A Note on Quadratic Forms and the u-invariant

1974 ◽  
Vol 26 (5) ◽  
pp. 1242-1244 ◽  
Author(s):  
Roger Ware
Keyword(s):  
Finite Number ◽  
Quadratic Forms ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Real Field ◽  
Witt Ring ◽  
Necessary And Sufficient

The u-invariant of a field F, u = u(F), is defined to be the maximum of the dimensions of anisotropic quadratic forms over F. If F is a non-formally real field with a finite number q of square classes then it is known that u ≦ q. The purpose of this note is to give some necessary and sufficient conditions for equality in terms of the structure of the Witt ring of F.

The Brascamp–Lieb Polyhedron

2010 ◽  
Vol 62 (4) ◽  
pp. 870-888 ◽  
Author(s):  
Stefán Ingi Valdimarsson
Keyword(s):  
Finite Number ◽  
Related Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Maps ◽  
Rank 2 ◽  
Necessary And Sufficient ◽  
Concise Description

AbstractA set of necessary and sufficient conditions for the Brascamp–Lieb inequality to hold has recently been found by Bennett, Carbery, Christ, and Tao. We present an analysis of these conditions. This analysis allows us to give a concise description of the set where the inequality holds in the case where each of the linear maps involved has co-rank 1. This complements the result of Barthe concerning the case where the linear maps all have rank 1. Pushing our analysis further, we describe the case where the maps have either rank 1 or rank 2.A separate but related problem is to give a list of the finite number of conditions necessary and sufficient for the Brascamp–Lieb inequality to hold. We present an algorithm which generates such a list.

scholarly journals Permutational Powers of a Graph

10.37236/8337 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Matteo Cavaleri ◽  
Daniele D'Angeli ◽  
Alfredo Donno
Keyword(s):  
Adjacency Matrix ◽  
Sufficient Conditions ◽  
Bipartite Graphs ◽  
Necessary And Sufficient Conditions ◽  
Permutation Matrix ◽  
Complete Bipartite Graphs ◽  
Necessary And Sufficient ◽  
Product Of Graphs

This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction recovers the classical zig-zag product of graphs when the permutation is an involution, and it is in fact more general. We start by discussing necessary and sufficient conditions on the permutation and on the adjacency matrix of a graph to guarantee their composition to represent an adjacency matrix of a graph, then we focus our attention on the cases in which the permutational power does not reduce to a zig-zag product. We show that the cases of interest are those in which the adjacency matrix is singular. This leads us to frame our problem in the context of equitable partitions, obtained by identifying vertices having the same neighborhood. The families of cyclic and complete bipartite graphs are treated in details.

scholarly journals Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$

2018 ◽  
Vol 37 (4) ◽  
pp. 9
Author(s):  
Naim L. Braha ◽  
Ismet Temaj
Keyword(s):  
Finite Number ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complex Numbers ◽  
Real Numbers ◽  
Tauberian Conditions ◽  
Necessary And Sufficient

Let $(x_k)$, for $k\in \mathbb{N}\cup \{0\}$  be a sequence of real or complex numbers and set $(EC)_{n}^{1}=\frac{1}{2^n}\sum_{j=0}^{n}{\binom{n}{j}\frac{1}{j+1}\sum_{v=0}^{j}{x_v}},$ $n\in \mathbb{N}\cup \{0\}.$  We present necessary and sufficient conditions, under which $st-\lim_{}{x_k}= L$ follows from $st-\lim_{}{(EC)_{n}^{1}} = L,$ where L is a finite number. If $(x_k)$ is a sequence of real numbers, then these are one-sided Tauberian conditions. If $(x_k)$ is a sequence of complex numbers, then these are two-sided Tauberian conditions.

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