One modulo N gracefulness of splitting graphs and subdivision of double triangle graphs

V. Ramachandran, C. Sekar


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 φ 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) φ is 1 − 1
(ii)φ induces a bijection φ* from the edge set of G to {1, N + 1, 2N + 1, . . . , N(q − 1) + 1}
where φ*(uv)=|φ(u) − φ(v)| . In this paper we prove that S’(P2n) , S’(P2n+1) , S’(K1,n) , all
subdivision of double triangular snakes (2Δk-snake) and all subdivision of 2mΔk-snake are one
modulo N graceful for all positive integers N.


Graceful, One modulo N graceful, Double triangular snakes


E.M.Badr and M.E.Abdel-aal, Odd gracefull labling for the subdivision of double triangles graphs,International Journal of Soft Computing, Mathematics and Control (IJSCMC), Vol.2, (2013).

R.B.Gnanajothi, Topics in Graph theory, Ph.D. Thesis, Madurai Kamaraj University, 1991.

S.W.Golomb, How to number a graph in Graph theory and computing R.C. Read, ed. Academic press, New York (1972) 23-27.

Joseph A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 18 (2011), #DS6.

V.Ramachandran and C.Sekar, One modulo N gracefulness of Acyclic graphs, Ultra Scientist of Physical Sciences, Vol.25, No (3)A, 417-424 (2013).

D. Moulton, Graceful labelings of triangular snakes, Ars Combin., 28 (1989) 3-13.

V. Ramachandran and C. Sekar, One modulo N gracefulness of Acyclic graphs, Ultra Scientist of Physical Sciences, Vol.25 No (3)A, 417-424 (2013).

A.Rosa, On certain valuations of the vertices of a graph, Theory of graphs.(International Symposium, Rome July 1966) Gordom and Breach, N.Y and Dunod, Paris (1967) 349-355.

A. Rosa, Cyclic Steiner Triple Systems and Labelings of Triangular Cacti, Scientia: Series A, 1 (1988) 87-95.

A. Rosa, Labelling snakes, Ars Combin., 3 (1977) 67-74.

C. Sekar, Studies in Graph theory, Ph.D. Thesis, Madurai Kamaraj University, 2002.

The DOI for this article will be: 10.12969/Scientia.Vol125.Sect2.Art04

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SCIENTIA International Identifiers: ISSN: 2282-2119 . DOI prefix: 10.12969 . EAN: 977-2282-211-00-9 . Handle (hdl) prefix: 11167

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