A vertex magic total labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers with the property that the sum of the label on the vertex and the labels of its incident edges is a constant, independent of the choice of the vertex. A graph with vertex magic total labeling with two constants or is called a vertex bimagic total labeling. The...

We consider undirected simple finite graphs. The sets of vertices and edges of a graph G are denoted by V (G) and E(G), respectively. For a graph G, we denote by δ(G) and η(G) the least degree of a vertex of G and the number of connected components of G, respectively. For a graph G and an arbitrary subset V0 ⊆ V (G) G[V0] denotes the subgraph of the graph G induced by the subset V0 of its verti...

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...

An a-labeling of a bipartite graph G with n edges easily yields both a cyclic G-decomposition of Kn,n and of K2nx+1 for all positive integers x. A ,B-Iabeling (or graceful labeling) of G yields a cyclic decomposition of K2n+1 only. It is well-known that certain classes of trees do not have a-Iabelings. In this article, we introduce the concept of a near a-labeling of a bipartite graph, and prov...

The graph exploration problem is to visit all the nodes of a connected graph by a mobile entity, e.g., a robot. The robot has no a priori knowledge of the topology of the graph or of its size. Cohen et al. [3] introduced label guided graph exploration which allows the system designer to add short labels to the graph nodes in a preprocessing stage; these labels can guide the robot in the explora...

Graph theory contains several topics, one of which will be discussed in this study is graph labeling. In the topic labeling, used a limited, simple, and undirected graph. study, type labeling total The multistar combination star graphs whose center vertex are not connected to each other. This research uses literature method divided into two parts, that basic calculation determine boundary first...

Nowadays, the problem of finding families graphs for which one may ensure existence a vertex-labeling and/or an edge-labeling based on certain class integers, constitutes challenge researchers in both number and graph theory. In this paper, we focus those vertex-labelings whose induced multiplicative assigns hyper totient numbers to edges graph. way, introduce characterize notions re...

The sets of vertices and edges of an undirected, simple, finite, connected graph G are denoted by V (G) and E(G), respectively. An arbitrary nonempty finite subset of consecutive integers is called an interval. An injective mapping φ : E(G) → {1, 2, . . . , |E(G)|} is called a labeling of the graph G. If G is a graph, x is its arbitrary vertex, and φ is its arbitrary labeling, then the set SG(x...

A p. q graph G = V,E is said to be a square graceful graph ifthere exists an injective function f: V G → 0,1,2,3,... , q such that the induced mapping fp : E G → 1,4,9,... , q 2 defined by fp uv = f u − f v is an injection. The function f is called a square graceful labeling of G. In this paper the square graceful labeling of the caterpillar S X1,X2 ,... ,Xn , the graphs Pn−1 1,2,...n ,mK1,n ∪ ...

In this paper we introduce a new type of labeling known as even vertex odd mean labeling. A graph G 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 ver...