Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set E(G) edge set. k natural numbers. For graph we define total k−labeling ρ such that vertices of are labeled with {0, 2, 4, . , 2kv} edges {1, 3, ke}, = max{2kv, ke}. Total called an irregular reflexive k− labeling if every two distinct have weights, weight defined as sum label incident to this edge. The minimum ha...

Let G be a finite simple graph with v vertices and e edges. A vertex-magic total labeling is a bijection λ from V (G)∪E(G) to the consecutive integers 1, 2, · · · , v+e with the property that for every x ∈ V (G), λ(x) + Σy∈N(x)λ(xy) = k for some constant k. Such a labeling is super if λ(V (G)) = {1, · · · , v}. We study some of the basic properties of such labelings, find some families of graph...

Let G be an Eulerian directed graph with an arc-labeling such that arcs going out from the same vertex have di erent labels. In this work, we present an algorithm to construct the Eulerian trail starting at an arbitrary vertex v of minimum lexicographical label among labels of all Eulerian trails starting at this vertex. We also show an application of this algorithm to construct the minimal de ...

We describe a method, based on vertex-labeling, to generate algorithms for manipulating the Hilbert space lling curve in the following ways: 1. Computing the image of a point in R. 2. Computing a pre-image of a point in R. 3. Drawing a nite approximation of the curve. 4. Finding neighbor cells in a decomposition ordered according to the curve. Our method is straightforward and exible, resulting...

The 2-step domination problem is to find a minimum vertex set D of a graph such that every vertex of the graph is either in D or at distance two from some vertex of D. In the present paper, by using a labeling method, we provide an O(m) time algorithm to solve the 2-step domination problem on block graphs, a superclass of trees.

A radio mean labeling of a connected graph G is a one to one map f from the vertex set V (G) to the set of natural numbers N such that for each distinct vertices u and v of G, d (u, v)+ ⌈ f(u)+f(v) 2 ⌉ ≥ 1+ diam (G). The radio mean number of f , rmn (f), is the maximum number assigned to any vertex of G.The radio mean number of G, rmn (G) is the minimum value of rmn (f) taken over all radio mea...

A difference vertex labeling of a graph G is an assignment f of labels to the vertices of G that induces for each edge xy the weight |f(x)− f(y)| . A difference vertex labeling f of a graph G of size n is odd-graceful if f is an injection from V (G) to {0, 1, ..., 2n − 1} such that the induced weights are {1, 3, ..., 2n − 1}. We show here that any forest whose components are caterpillars is odd...

A graph G is k–weighted–list–antimagic if for any vertex weighting ω : V (G) → R and any list assignment L : E(G)→ 2R with |L(e)| ≥ |E(G)|+k there exists an edge labeling f such that f(e) ∈ L(e) for all e ∈ E(G), labels of edges are pairwise distinct, and the sum of the labels on edges incident to a vertex plus the weight of that vertex is distinct from the sum at every other vertex. In this pa...

A graph is called supermagic if it admits a labeling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we establish some conditions for graphs with a saturated vertex to be supermagic. Inter alia we show that complete multipartite graphs K1,n,n and K1,2,...,2 are supe...

A total k-labeling is a function fe from the edge set to {1, 2, . , ke} and fv vertex {0, 4, 2kv}, where k = max{ke, 2kv}. distance irregular reflexive of graph G k-labeling, if for every two different vertices u 0 G, w(u) 6= w(u ), Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum which has k-labelling called strength denoted by Dref (G). In this paper, we determine exact value some connected graph...