A graph with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f:V(G){0, 2, 4, ... 2q-2,2q} such that the induced map f*: E(G) {1, 3, 5, ... 2q-1} defined by f*(uv)=     f u f v 2  is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. In this paper we pay our attention to p...

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 for each edge xy assign the label ⌈ f(x)+f(y) 2 ⌉ where x, y ∈ V (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,...

In this paper, we introduce a new labeling called one modulo three harmonic mean labeling. A graph G is said to be one modulo three harmonic mean graph if there is a function φ from the vertex set of G to {1, 3, 4, ... ,3 − 2, 3 } with φ is one-one and φ induces a bijection φ∗ from the edge set of G to {1, 4, ..., 3q 2}, where φ∗(e = uv) = ( ) ( ) ( ) ( ) or ( ) ( ) ( ) ( ) and the function φ i...

let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...

a graph of size n is said to be graceful when is possible toassign distinct integers from {0, 1, . . . , n} to its verticesand {|f(u)−f(v)| : uv ∈ e(g)} consists of n integers. inthis paper we present broader families of graceful graphs; these families are obtained via three different operations: the third power of a caterpillar, the symmetric product of g and k2 , and the disjoint :union: of g...