Let G = (V,E) be a graph of order n. A distance magic labeling of G is a bijection l : V → {1, 2, . . . , n} for which there exists a positive integer k such that ∑ x∈N(v) l(x) = k for all v ∈ V , where N(v) is the open neighborhood of v. In this paper we deal with circulant graphs C(1, p). The circulant graph Cn(1, p) is the graph on the vertex set V = {x0, x1, . . . , xn−1} with edges (xi, xi...

“Super-resolution” is the term used to denote the subset of imaging processing that tries to estimate a high-resolution image of a scene, given a set of low-resolution observations (Fig. 1). Colloquially, when superresolution researchers try to describe what they do to family, friends, and loved ones, we can use the example from the TV show CSI: whenever someone on CSI looks at low-resolution s...

A 1-vertex-magic vertex labeling of a graph G(V,E) with p vertices is a bijection f from the vertex set V (G) to the integers 1, 2, . . . , p with the property that there is a constant k such that at any vertex x the sum ∑ f(x) taken over all neighbors of x is k. In this paper, we study the 1-vertex-magic vertex labelings of two families of disconnected graphs, namely a disjoint union of m copi...

We establish concentration inequalities for Lipschitz functions of dependent random variables, whose dependencies are specified by forests. also give results decomposable functions, improving Janson’s Hoeffding-type inequality the summation graph-dependent bounded variables. These extend McDiarmid’s difference to cases.

In this paper we prove that the wrapped Butterry graph WBF(d;n) of degree d and dimension n is decomposable into Hamilton cycles. This answers a conjecture of D. Barth and A. Raspaud who solved the case d = 2.

Abstract: Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs. This is achieved through dimensionality expansion that causes the graph nodes to be conditionally independent given a latent tree. The Markov updat...

Let the matching polynomial of a graph G be denoted by μ(G, x). A graph G is said to be θ-super positive if μ(G, θ) 6= 0 and μ(G \ v, θ) = 0 for all v ∈ V (G). In particular, G is 0-super positive if and only if G has a perfect matching. While much is known about 0-super positive graphs, almost nothing is known about θsuper positive graphs for θ 6= 0. This motivates us to investigate the struct...

We show in this paper that the circulant graph G( 2”‘, 4) is Hamiltonian decomposable, and propose a recursive construction method. This is a partial answer to a problem posed by B. Alspach. @ 1997 Published by Elsevier Science B.V.

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

The motivation for this paper is the integer linear programming approach to learning the structure of a decomposable graphical model. We have chosen to represent decomposable models by means of special zero-one vectors, named characteristic imsets. Our approach leads to the study of a special polytope, defined as the convex hull of all characteristic imsets for chordal graphs, named the chordal...