Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...

We present here prime cordial labeling for the graphs obtained by some graph operations on cycle related graphs.

A graph G is said to have totally magic cordial(TMC) labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0)− nf (1)| ≤ 1, where nf (i)(i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we investigate some new families of graphs that admit totally magic cordial labeli...

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...

For a graph G = (V,E) with a binary vertex coloring f : V (G)→ Z2, let vf (i) = |f−1(i)|. We say f is friendly if |vf (1) − vf (0)| ≤ 1, i.e., the number of vertices labeled 1 is the same or almost the same as the number of vertices labeled 0. The coloring f induces an edge labeling f ∗ : E(G) → Z2 defined by f ∗(uv) = f(u) + f(v) (mod 2), for each uv ∈ E(G). Let ef (i) = |{uv ∈ E(G) : f ∗(uv) ...

A Total Mean Cordial labeling of a graph G = (V,E) is a mapping f : V (G) → {0, 1, 2} such that f(xy) = ⌈