an h-magic labeling in a h-decomposable graph g is a bijection f : v (g) ∪ e(g) → {1, 2, ..., p + q} such that for every copy h in the decomposition, σνεv(h) f(v) +  σeεe(h) f(e) is constant. f is said to be h-e-super magic if f(e(g)) = {1, 2, · · · , q}. a family of subgraphs h1,h2, · · · ,hh of g is a mixed cycle-decomposition of g if every subgraph hi is isomorphic to some cycle ck, for k ≥ ...

A graph G is called a 1-planar graph if it can be drawn on the plane so that each edge includes at most one crossing. It is not so difficult to see that |E(G)| ≤ 4|V (G)| − 8 for any 1-planar graph. In particular, a 1-planar graph G is said to be optimal if the equality holds. Suzuki has already proved that there exists an optimal 1-planar graph which can be embedded on the orientable closed su...

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called local edge antimagic labeling if for any two adjacent edges e uv e’ vw G, we have w(e) ≠ w(e’), where the weight w(e uv) f(u)+f(v) w(e’) f(v)+f(w). has labeling. The chromatic number χ’lea(G) defined to minimum colors taken over all colorings induced by labelings G. In thi...

let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...