AUTHOR AND 
V. RAMACHANDRAN1 and C. SEKAR2 
KEYWORDS: 
Graceful, modulo N graceful, Path, Sm,n , Sm,n Sm,n, Caterpillar, Star, Lobster, Banana tree and Rooted tree ofheight two AMS Subject Classification (2010):05C78 
Issue Date: 
December 2013 
Pages: 

ISSN: 
23198044 (Online) – 2231346X (Print) 
Source: 
Vol.25 – No.3 
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DOI: 
juspsA 
ABSTRACT:
A function f is called a graceful labelling of a graph G with q edges if f is an injection from the vertices of G to the set (0, 1, 2,…, q) such that, when each edge xy is assigned the label  f(x) — f(y), the resulting edge labels are distinct. A graph G is said to be one modulo N graceful (where N is a positive integer) if there is a function from the vertex set
of G to {0, 1. N, (N + 1), 2N, (2N + 1),…, N(q – 1). N(q 1) + 1} in such a way that (i) is 11 (ii) induces a bijection * from the edge set of G to {1, N+1, 2N +1,…, N(q – 1)+1} where *(uv) = (u)  (v). In this paper we prove that the acyclic graphs viz. Paths, Caterpillars, Stars and S2,n S2,n are one modulo N graceful for all positive integer N; Lobsters, Banana trees and Rooted tree of height two are one modulo N graceful for N > 1. where Sm,n Sm,n is a graph obtained by identifying one pendant vertex of each Sm,n. This is a fire cracker of subdivisioned stars.
Copy the following to cite this Article:
V. RAMACHANDRAN1 and C. SEKAR2, “One modulo N gracefulness of acyclic graphs”, Journal of Ultra Scientist of Physical Sciences, Volume 25, Issue 3, Page Number , 2016
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V. RAMACHANDRAN1 and C. SEKAR2, “One modulo N gracefulness of acyclic graphs”, Journal of Ultra Scientist of Physical Sciences, Volume 25, Issue 3, Page Number , 2016
Available from: http://www.ultrascientist.org/paper/189/
A function f is called a graceful labelling of a graph G with q edges if f is an injection from the vertices of G to the set (0, 1, 2,…, q) such that, when each edge xy is assigned the label  f(x) — f(y), the resulting edge labels are distinct. A graph G is said to be one modulo N graceful (where N is a positive integer) if there is a function from the vertex set
of G to {0, 1. N, (N + 1), 2N, (2N + 1),…, N(q – 1). N(q 1) + 1} in such a way that (i) is 11 (ii) induces a bijection * from the edge set of G to {1, N+1, 2N +1,…, N(q – 1)+1} where *(uv) = (u)  (v). In this paper we prove that the acyclic graphs viz. Paths, Caterpillars, Stars and S2,n S2,n are one modulo N graceful for all positive integer N; Lobsters, Banana trees and Rooted tree of height two are one modulo N graceful for N > 1. where Sm,n Sm,n is a graph obtained by identifying one pendant vertex of each Sm,n. This is a fire cracker of subdivisioned stars.