The objective of this paper is to present a new class of odd graceful graphs. In particular, we show that the linear cyclic snakes (1, k) C4snake and (2, k) C4snake are odd graceful. We prove that the linear cyclic snakes (1, k) C6snake and (2, k) C6snake are odd graceful. We also prove that the linear cyclic snakes (1, k) C8snake and (2, k) C8snake are odd graceful. We generalize the above res...

R. B. Gnanajothi, Topics in graph theory, Ph. D. thesis, Madurai Kamaraj University, India, 1991. E. M. Badr, On the Odd Gracefulness of Cyclic Snakes With Pendant Edges, International journal on applications of graph theory in wireless ad hoc networks and sensor networks (GRAPH-HOC) Vol. 4, No. 4, December 2012. E. M. Badr, M. I. Moussa & K. Kathiresan (2011): Crown graphs and subdivision of l...

A graph G= (V,E) with p vertices and q edges is called a Harmonic mean graph if it is possible to label the vertices xV with distinct labels f(x) from 1,2,....,q+1 in such a way that when each edge e=uv is labeled with f(uv)= ( ) ( ) ( ) ( ) (or) ( ) ( ) ( ) ( ) , then the edge labels are distinct. In this case, f is called Harmonic mean labeling of G. In this paper we prove that Double Triang...

Let G = (V,E) be a graph with p vertices and q edges. G is said to have skolem difference mean labeling if it is possible to label the vertices x ∈ V with distinct elements f(x) from 1, 2, 3, ..., p+ q in such a way that for each edge e = uv, let f∗(e) = l |f(u)−f(v)| 2 m and the resulting labels of the edges are distinct and are from 1, 2, 3, ..., q. A graph that admits a skolem difference mea...

In this paper some new type of odd graceful graphs are investigated. We prove that the graph obtained by joining a cycle C8 with some star graphs S1,r keeping one vertex and three vertices gap between pair of vertices of the cycle admits odd graceful labelling. We also prove that the graph obtained by joining a cycle C12 with some star graphs S1,r keeping two, three and five vertices gap betwee...

In this paper, we introduce a new labeling called one modulo three mean labeling. A graph G is said to be one modulo three mean graph if there is an injective function φ from the vertex set of G to the set {a | 0 ≤ a ≤ 3q2 and either a≡0(mod 3) or a≡1(mod 3) } where q is the number of edges of G and φ induces a bijection φ * from the edge set of G to { } |1 3 2 and ( 3) a a q a 1 mod ≤ ≤ − ≡ gi...

An antimagic labeling of a graph G with m edges is a bijection from E(G) to {1, 2, . . . ,m} such that for all vertices u and v, the sum of labels on edges incident to u differs from that for edges incident to v. Hartsfield and Ringel conjectured that every connected graph other than the single edge K2 has an antimagic labeling. We prove this conjecture for regular graphs of odd degree.