Let G be a graph of size n with vertex set V (G) and edge set E(G). A ρlabeling of G is a one-to-one function h : V (G) → {0, 1, . . . , 2n} such that {min{|h(u)−h(v)|, 2n+1−|h(u)−h(v)|} : {u, v} ∈ E(G)} = {1, 2, . . . , n}. Such a labeling of G yields a cyclicG-decomposition ofK2n+1. It is known that 2-regular bipartite graphs, the vertex-disjoint union of C3’s, and the vertex-disjoint union o...

Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper ...

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

In this paper we introduce remainder cordial labeling of graphs. Let $G$ be a $(p,q)$ graph. Let $f:V(G)rightarrow {1,2,...,p}$ be a $1-1$ map. For each edge $uv$ assign the label $r$ where $r$ is the remainder when $f(u)$ is divided by $f(v)$ or $f(v)$ is divided by $f(u)$ according as $f(u)geq f(v)$ or $f(v)geq f(u)$. The function$f$ is called a remainder cordial labeling of $G$ if $left| e_{...

A shell graph is the join of a path P k of 'k' vertices and K 1. A subdivided shell graph can be constructed by subdividing the edges in the path of the shell graph. In this paper we prove that the disjoint union of two subdivided shell graphs is odd graceful and also one modulo three graceful. 1. Introduction A graph labeling is an assignment of integers to the vertices or edges, or both, subj...

Graphs that have the properties of odd harmonious labeling are graphs. The research objective this paper is to obtain on layered graph C(x,y) and D(x,y). used in a qualitative method. flow consists data collection, processing, analysis. collection stage constructing definition new class graph, processing vertex edge labeling, analysis theorem proving it. results show D(x,y) fulfill labeling. Su...

Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious \cite{Hovey}. If $A$ is an Abelian group, then labeling $f \colon V (G) \rightarrow A$ the vertices some graph $G$ induces edge on $G$; $uv$ receives label (u) + f (v)$. A if there vertex-labeling such that (1) vertex classes differ in size by at most one (2) induced one. Patrias Pechenik studied larger class f...

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 function f is called an odd-even graceful labeling of a graph G if f: V(G) → {0,1,2,...,q} is injective and the induced function f : E(G) → { { 0,2,4,...,2q+2i/i= 1 to n} such that when each edge uv is assigned the label |f(u) – f(v)| the resulting edge labels are {2,4,6,...,2q}. A graph which admits an odd-even graceful labeling is called an odd-even graceful graph. In this paper, the odd-ev...