We consider the problem of learning a labeled graph from a given family of graphs on n vertices in a model where the only allowed operation is to query whether a set of vertices induces an edge. Questions of this type are motivated by problems in molecular biology. In the deterministic nonadaptive setting, we prove nearly matching upper and lower bounds for the minimum possible number of querie...

An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is local antimagic if vertex-weights are distinct for pair neighboring vertices, where vertex-weight sum labels all edges incident with that vertex. Any induces proper vertex coloring G color its vertex-weight. This naturally leads to concept chromatic number. The number defined be minimum colors take...

Let G be a graph with the vertex set V (G), edge set E(G). A vertex labeling is a bijection f : V (G)→ {1, 2, . . . , |V (G)|}. The weight of e = uv ∈ E(G) is given by g(e) = min{f(u), f(v)}. The min-sum vertex cover (msvc) is a vertex labeling that minimizes the vertex cover number μs(G) = ∑ e∈E(G) g(e). The minimum such sum is called the msvc cost. In this paper, we give both general bounds a...

An edge labeling of a graph G = (V,E) is a bijection from the set of edges to the set of integers {1, 2, . . . , |E|}. The weight of a vertex v is the sum of the labels of all the edges incident with v. If the vertex weights are all distinct then we say that the labeling is vertex-antimagic, or simply, antimagic. A graph that admits an antimagic labeling is called an antimagic graph. In this pa...

A vertex-magic group edge labeling of a graph G(V,E) with |E| = n is an injection from E to an abelian group Γ of order n such that the sum of labels of all incident edges of every vertex x ∈ V is equal to the same element μ ∈ Γ. We completely characterize all Cartesian products Cn Cm that admit a vertex-magic group edge labeling by Z2nm, as well as provide labelings by a few other finite abeli...

Antimagic labeling of a graph with vertices and edges is assigned the labels for its by some integers from set , such that no two received same label, weights are pairwise distinct. Where vertex-weights vertex under this sum all incident to vertex, in paper, we deal problem finding antimagic edge special families graphs called strong face graphs. We prove antimagic, ladder wheel fan prism final...

This paper proposes a statistical approach to labeling images using a more natural graphical structure than the pixel grid (or some uniform derivation of it such as square patches of pixels). Typically, low-level vision estimations based on graphical models work on the regular pixel lattice (with a known clique structure and neighborhood). We move away from this regular lattice to more meaningf...

a set $s$ of vertices in a graph $g=(v,e)$ is called a total$k$-distance dominating set if every vertex in $v$ is withindistance $k$ of a vertex in $s$. a graph $g$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (g - x) < gamma_{t}^{k}(g)$ for any vertex $xin v(g)$. in this paper,we investigate some results on total $k$-distance domination-critical of graphs.

Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling$fcolon V(D)to {0, 1, 2}$such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ ofRoman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,is called a {em Roman dominating family} (of functions) on $D$....