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...

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 ...

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, ....

Let G = G(V, E) be a finite simple undirected graph with vertex set V and edge set E, where |E| and |V | are the number of edges and vertices on G. An (a, d)-edge antimagic vertex ((a, d)-EAV) labeling is a one-toone mapping f from V (G) onto {1, 2, . . . , |V |} with the property that for every edge xy ∈ E, the edge-weight set is equal to {f(x) + f(y) : x, y ∈ V } = {a, a+ d, a+2d, . . . , a+(...

Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

Let is a simple and connected graph with as vertex set edge set. Vertex labeling on inclusive local irregularity coloring defined by mapping the function of . In other words, an so that its weight value obtained adding up labels neighboring label. The chromatic number minimum colors from in G, denoted this paper, we learn about determine book graphs.

Let be a connected graph with vertex set and edge . A bijection from to the is labeling of The called rainbow antimagic if for any two in path , where Rainbow coloring which has labeling. Thus, every induces G weight color connection number smallest colors all colorings denoted by In this study, we studied have an exact value joint product