Journal of Algorithms and Computation
Volume:45 Issue: 1, Dec 2014

In this paper we define a new labeling called skolem odd difference mean labeling and investigate skolem odd difference meanness of some standard graphs. Let G = (V,E) be a graph with p vertices and q edges. G is said be skolem odd difference mean if there exists a function f : V (G) → {0, 1, 2, 3, . . . , p + 3q − 3} satisfying f is 1−1 and the induced map f : E(G) → {1, 3, 5, . . . , 2q−1} denoted by f*(e) =|f(u)−f(v)|/2 is a bijection. A graph that admits skolem odd difference mean labeling is called odd difference mean graph. We call skolem odd difference mean labeling as skolem even vertex odd difference mean labeling if all the vertex labels are even.the formula is not displayed correctly!

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 and Pm, where G is a special type of graceful graph named - graph. Moreover, the majority of the graceful labelings obtained here correspond to the most restrictive kind, they are -labelings. These labelings are in the core of this research area due to the fact that they can be used to create other types of graph labelings, almost independently of the nature of these labelings.the formula is not displayed correctly!

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} according as p is even or odd. A graph which admits edge pair sum labeling is called an edge pair sum graph. In this paper we exhibit some spider graph.the formula is not displayed correctly!

Mean labelings are a type of additive vertex labeling. This labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. In this paper we focus on mean labelings of some graphs that are the result of the corona operation. In particular we prove the existence of mean labelings for graphs of the form G ⊙ mK1 in the cases where G is an even cycle or G is an α-mean graph of odd size and the cardinalities of its stable sets differ by at most one unit. Under these conditions, we prove that G ⊙ P2 and G ⊙ P3 are also mean graphs, and that the class of α-graphs is equivalent to the class of α-mean graphs.