A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting $\omega\colon V(G)\to\mathbb{R}$ and list assignment $L\colon E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling $f$ such that $f(e)\in L(e)$ all $e\in E(G)$, labels of edges are pairwise distinct, the sum on incident to a plus weight distinct from at every other vertex. In this paper we prove ...

Let ( , ) G V E be a simple graph. For a total labeling { } : 1,2,3,..., V E k ∂ ∪ → the weight of a vertex x is defined as ( ) ( ) ( ). xy E wt x x xy ∈ = ∂ + ∂ ∑ ∂ is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y, ( ) ( ). wt x wt y ≠ . The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularit...

The Graceful Tree Conjecture claims that every finite simple tree of order n can be vertex labeled with integers {1, 2, ...n} so that the absolute values of the differences of the vertex labels of the end-vertices of edges are all distinct. That is, a graceful labeling of a tree is a vertex labeling f , a bijection f : V (Tn) −→ {1, 2, ...n}, that induces an edge labeling g(uv) = |f(u)− f(v)| t...

For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . . , |V (G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total label...

The local antimagic total vertex labeling of graph G is a that every vertices and edges label by natural number from 1 to such two adjacent has different weights, where sum the labels all incident vertex. If start smallest then edge so kind coloring called super labeling. That induces for v, weight w(v) color v. minimum colors obtained chromatic G, denoted χlsat(G). In this paper, we consider G...

We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic oriented triangular embeddings of a complete graph on 12s + 7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labell...

A total labeling of a graph G is a bijection from the vertex set and edge set of G onto the set {1, 2, . . . , |V (G)| + |E(G)|}. Such a labeling ξ is vertex-antimagic (edge-antimagic) if all vertex-weights wtξ(v) = ξ(v) + ∑ vu∈E(G) ξ(vu), v ∈ V (G), (all edge-weights wtξ(vu) = ξ(v) + ξ(vu) + ξ(u), vu ∈ E(G)) are pairwise distinct. If a labeling is simultaneously vertex-antimagic and edge-antim...

An odd graceful labeling of a graph ( , ) G V E = is a function : ( ) {0,1,2, . . .2 ( ) 1} f V G E G → − such that | ( ) ( )| f u f v − is odd value less than or equal to 2 ( ) 1 E G − for any , ( ) u v V G ∈ . In spite of the large number of papers published on the subject of graph labeling, there are few algorithms to be used by researchers to gracefully label graphs. This work provides gene...

Let be a connected graph with vertex set and edge . The bijective function is said to labeling of where the associated weight for If every has different weight, called an antimagic labeling. A path in vertex-labeled , two edges satisfies rainbow path. if vertices there exists Graph admits coloring, we assign each color smallest number colors induced from all weights connection denoted by In thi...

A graph with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f:V(G){0, 2, 4, ... 2q-2,2q} such that the induced map f*: E(G) {1, 3, 5, ... 2q-1} defined by f*(uv)=     f u f v 2  is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. In this paper we pay our attention to p...