Proyecciones Journal of Mathematics Vol. 31, N^o 3, pp. 261-275, September 2012. Universidad Católica del Norte Antofagasta - Chile

Symmetric regular cacti-properties and enumeration

 

S. K. Vaidya

Saurashtra University, India

D. D. Bantva

L. E. College, India

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ABSTRACT

A cactus is a connected graph whose all the blocks are isomorphic to cycle or complete graph on n vertices. We introduce symmetric regular cacti and a procedure for their construction. We discuss some characteristics of symmetric regular cacti. The number of symmetric regular cacti on given number of vertices are also enumerated. A possible application of present work to a real world problem for the committee formation is also suggested.

Keywords : Block, cactus, cut vertex.

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REFERENCES

[1] J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, j|DS6, 18 : 12 and 49, (2011).         [ Links ]

[2] S. K. Vaidya, D. D. Bantva, Labeling cacti with a condition at distance two, Le Mathematiche, 66 : pp. 29-36, (2011).         [ Links ]

[3] D. B. West, Introduction to Graph Theory, Prentice -Hall of India, (2001).         [ Links ]

S. K. Vaidya

Department of Mathematics Saurashtra University, Rajkot - 360005 Gujarat

INDIA

e-mail : samirkvaidya@yahoo.co.in

D. D. Bantva

Department of Mathematics

L. E. College, Morvi - 363642

Gujarat

INDIA

e-mail : devsi.bantva@gmail.com

Received : March 2012. Accepted : June 2012