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. The problem graphs can be naturally ext...

A Sum divisor cordial labeling of a graph G with vertex set V is bijection r from to {1,2,3,...,|V (G )|} such that an edge uv assigned the label 1 if 2 divides r(u)+ (v ) and 0 otherwise; number edges labeled 1differ by at most . sum called graph. In this research paper, we investigate bahevior for Grötzsch graph, fusion any two vertices in duplication arbitrary switching degree four three pat...

a graph g = (v,e) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : v (g) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ v (g), xy ∈ e(g), and the total number of 0, 1 and 2 are balanced. that is |evf (i) − evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). in thi...

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 ...

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a function. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if ∣

A graph G(V,E) with vertex set V is said to have a prime labeling if its vertices are labeled with distinct integers 1, 2, . . . , |V | such that for each edge xy ∈ E the labels assigned to x and y are relatively prime. A prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, . . . , |V |} such that if each edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 ...

In this paper we investigate the pair difference cordial labeling
 behavior of Certain broken wheel graphs.

As part of the largest, longest running prospective American study of same-sex parent families, the present investigation examined relationship dissolution in planned lesbian families. Data were collected from 40 separated couples and their 17-year-old adolescent offspring—19 girls and 21 boys. Nearly all breakups occurred before the former couples could have obtained the legal equivalent of sa...