Call for Paper - January 2023 Edition
IJCA solicits original research papers for the January 2023 Edition. Last date of manuscript submission is December 20, 2022. Read More

Independent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes

Print
PDF
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Authors:
Chris Monica M., D. Little Femilin Jana
10.5120/ijca2017913936

Chris Monica M. and Little Femilin D Jana. Independent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes. International Journal of Computer Applications 165(7):46-48, May 2017. BibTeX

@article{10.5120/ijca2017913936,
	author = {Chris Monica M. and D. Little Femilin Jana},
	title = {Independent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes},
	journal = {International Journal of Computer Applications},
	issue_date = {May 2017},
	volume = {165},
	number = {7},
	month = {May},
	year = {2017},
	issn = {0975-8887},
	pages = {46-48},
	numpages = {3},
	url = {http://www.ijcaonline.org/archives/volume165/number7/27589-2017913936},
	doi = {10.5120/ijca2017913936},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W is called the independent resolving number and is denoted by ir(G). In this paper, we determine the independent resolving number of Fibonacci Cubes and Extended Fibonacci cubes.

References

  1. Saenpholphat, V., Zhang, P., Conditional resolvability of graphs: a survey. IJMMS vol. 38, pp. 1997–2017, 2003.
  2. Z. Beerliova, F. Eberhard, T. Erlebach, A. Hall, M. Hoffman and M. Mihalak, Network Discovery and Verification, IEEE Journal on Selected Areas in Communications, Vol.24, No. 12, pp. 2168-2181, 2006.
  3. Slater, P.J., Leaves of trees. Congr. Numer., 14, pp. 549–559, 1975.
  4. Y. Saad and M.H. Schultz, Topological Properties of Hypercubes, IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, 1988.
  5. Hsu, W. J., Fibonacci cubes - a new interconnection topology, IEEE Trans. Parallel and Distributed Systems, 4, no.1, pp. 3-12, 1993.
  6. Hsu, W. J., Fibonacci cubes - Properties of an Asymmetric Interconnection Topology, Proc. Inter. Conf. on Parallel Processing, pp. 1249-1268, 1991.
  7. J.Wu., Extended Fibonacci Cubes, IEEE Trans. Parallel and Distributed Systems, vol.8, no.12, pp. 1203-1210,1997.
  8. Ioana zelina, A survey on cycles embeddings in Fibonacci and extended Fibonacci cubes, Creative Math. & Inf., vol. 17, no. 3, pp. 548 – 554, 2008.

Keywords

Resolving set, Independent resolving number, Fibonacci Cubes, Extended Fibonacci Cubes, Hamming distance.