Let G(V,E) be a graph and λ be a bijection from the set V ∪E to the set of the first |V |+ |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s, d) -vertex antimagic total (VAT) labeling if the vertex weights form an arithmetic pro...

A vertex bimagic 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 1, 2, 3, ...v + e with the property that the sum of the label on the vertex and the labels of its incident edges is one of the constants k1 or k2, independent of the choice of the vertex. In this paper we have discussed that bistar Bn,n are vertex bimagic to...

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...

Let $A$ be an abelian group. A graph $G=(V,E)$ is said to be $A$-barycentric-magic if there exists a labeling $l:E(G)longrightarrow Asetminuslbrace{0}rbrace$ such that the induced vertex set labeling $l^{+}:V(G)longrightarrow A$ defined by $l^{+}(v)=sum_{uvin E(G)}l(uv)$ is a constant map and also satisfies that $l^{+}(v)=deg(v)l(u_{v}v)$ for all $v in V$, and for some vertex $u_{v}$ adjacent t...

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...

Let G = ( V , E ) be a simple undirected graph. A labeling f : )→{1, …, k } is local inclusive d -distance vertex irregular of if every adjacent vertices x y ∈ have distinct weights, with the weight w ), sum labels whose distance from at most . The irregularity strength lidis least number for which there exists In this paper, we prove conjecture on 1 tree and generalize result block graph using...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

Let G(V, E) be a graph with order n no component of 2. An edge k-labeling α: E(G) →{1,2,…,k} is called modular irregular G if the corresponding weight function wt_ α:V(G) → Z_n defined by α(x) =Ʃ_(xyϵE(G)) α(xy) bijective. The value wt_α(x) vertex x. Minimum k such that has irregularity strength G. In this paper, we define labeling on C_n⊙mK_1. Furthermore, determine C_n⊙mK_1.Keywords: corona p...

A vertex-magic total labeling on a graph G is a one-to-one map λ from V (G) ∪E(G) onto the integers 1, 2, · · · , |V (G) ∪E(G)| with the property that, given any vertex x, λ(x) + ∑ y∼x λ(y) = k for some constant k. In this paper we completely determine which complete bipartite graphs have vertex-magic total labelings.