Edge Reduced Skolem Difference Mean Number of Some Graphs

ABSTRACT
A graph G = (𝑉, 𝐸) with p vertices and q edges is said to have skolem difference mean labeling
if it is possible to label the vertices x 𝜖 𝑉 with distinct elements f (𝑥) from {1,2,3, … , 𝑝 + 𝑞} in such a
way that the edge e = 𝑢𝑣 is labeled with |𝑓(𝑢)−𝑓(𝑣)|2if |𝑓(𝑢) − 𝑓(𝑣)| is even and |𝑓(𝑢)−𝑓(𝑣)|+12 if
|𝑓(𝑢) − 𝑓(𝑣)| is odd and the resulting labels of the edges are distinct and are from {1,2,3, … , 𝑞}. A
graph that admits skolem difference mean labeling is called a skolem difference mean graph. In this
paper, the author studied the edge reduced skolem difference mean number of some graphs.

References
[1] B. D. Acharya, Construction of certain infinite families of graceful graphs from a given
graceful graph, Def. Sci. J. 32(3) (1982) 231-236.
[2] B. D. Acharya, S. B. Rao and S. Arumugam, Embedding and NP-complete problems for
graceful graphs, Proc. Labelings of discrete structures and applications, (Eds: B.D.
Acharya, S. Arumugam, A. Rosa) Narosa Publishing House, 2008, 57-62.
[3] Frank Harary, Graph Theory, Narosa Publishing House, New Delhi, 2001.
[4] Joseph A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of
Combinatorics, 15(2008), #DS6.
[5] K. Murugan and A. Subramanian, Labeling of Sub divided graphs, American Journal of
Mathematics and Sciences, 1(1) (2012) 143-149.
[6] K. Murugan and A. Subramanian, Skolem difference mean graphs, Mapana Journal of
Sciences, 11(4) (2012) 109-120.
[7] K. Murugan and A. Subramanian, Skolem difference mean labeling of H-graphs,
International Journal of Mathematics and Soft Computing, 1(1) (2011)115-129.
[8] K. Murugan, Some results on skolem difference mean graphs, International Journal of
Mathematics and its Applications, 3(3D) (2015) 75-80.
[9] D. Ramya, M. Selvi and R. Kalaiyarasi, On skolem difference mean labelling of graphs,
International Journal of Mathematical Archive, 4(12) (2013) 73-79.
[10] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs
(International symposium, Rome, July1966), Gorden and Breach, N.Y and Dunod
Paris, 1967, 349-355.
[11] Sampathkumar E. and Walikar H. G, On the splitting graph of a graph, The Karnataka
University Journal Science, Vol. XXX & XXXI (combined) (1980-1981).
[12] M.Selvi and D.Ramya, On skolem difference mean labelling of some trees,
International Journal of Mathematics and Soft Computing, 4(2) 2014) 11-18.
[13] M. Selvi, D. Ramya and P. Jeyanthi, Skolem difference mean graphs, Proyecciones
Journal of Mathematics, 34(3) (2015) 243-254.
[14] S. K. Vaidya and N. H. Shah, Some new odd harmonious graphs, International Journal
of Mathematics and Soft Computing, 1(1) (2011) 9-11.
[15] S. K. Vaidya and P. L. Vihol, Fibonacci and Super Fibonacci graceful labeling of some
graphs, Studies in Mathematical Sciences, 2(2) (2011) 24-35.

Download all article in PDF

WSN 30 (2016) 129-142