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...

For a simple graph G with vertex set V (G) and edge set E(G), a labeling φ : V (G) ∪ E(G) −→ {1, 2, . . . , k} is called a vertex irregular total klabeling of G if for any two different vertices x and y, their weights wt(x) ∗ The work was supported by the Higher Education Commission Pakistan. 148 A. AHMAD, K.M. AWAN, I. JAVAID AND SLAMIN and wt(y) are distinct. The weight wt(x) of a vertex x in...

The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling   with $d$ labels  that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...

Let G be a graph with p vertices and q edges an injective function, where k is positive integer. If the induced edge labeling defined by for each bijection, then f called odd Fibonacci irregular of G. A which admits graph. The irregularity strength ofes(G) minimum labeling. In this paper, some subdivision graphs obtained from vertex identification determined.

This paper deals with two types of graph labelings namely, the super (a, d)-edge antimagic total labeling and super (a, d)-vertex antimagic total labeling on the Harary graph C n. We also construct the super edge-antimagic and super vertex-antimagic total labelings for a disjoint union of k identical copies of the Harary graph.

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge ...

A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...

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) = (sigma 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, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

Let G(V,E) be a graph with p vertices and q edges. A vertex labeling of G is an assignment f : V (G) → {1, 2, 3, . . . , p + q} be an injection. For a vertex labeling f, the induced Smarandachely edge m-labeling f S for an edge e = uv, an integer m ≥ 2 is defined by f ∗ S(e) = ⌈ f(u) + f(v) m ⌉ . Then f is called a Smarandachely super m-mean labeling if f(V (G))∪ {f(e) : e ∈ E(G)} = {1, 2, 3, ....