Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P520
A graph G = (V,E) is complementary distance pattern uniform (CDPU), if there exists M V(G) such that fM(u) = {d(u,v) : v ε M}, for every u ε V(G) - M, is independent of the choice of u ε V(G) - M and the set M is called the CDPU set. In this paper, we extend the notion of CDPU sets into hypergraphs. As every graph admits a CDPU set and a graph has more than one CDPU set, we can construct a hypergraph corresponding to that graph with the same vertex set and edge set corresponds to the different CDPU sets of a graph G.
[1] B.D. Acharya, Contributions to the Theories of Graphs,Graphoids and Hypergraphs, The Indian Institute of Technology, Bombay, 1975.
[2] B.D. Acharya, Interrelations among the notions of independence, domination and full sets in a hypergraph, Nat. Acad. Sci. Letters, Vol.13, No.11, 1990.
[3] B.D. Acharya and M. Lasvergnas, Hypergraphs with cyclomatic number zero, triangulated graphs, and an inequality, J. Combin.Theory, B.33 (1982), 52-56.
[4] C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam,1973.
[5] C. Berge, Hypergraphs: Combinatorics of Finite Sets, North-Holland, Amsterdam, 1989.
[6] M. Buratti, G. Burosch and P.V. Ceccherint,A characterization of hypergraphs which areproducts of a finite number of edges, Rendiconti diMatematica, Serie VII Volume 17, Roma (1997),373-385.
[7] Germina K.A., Beena Koshy, Complementary Distance Pattern Uniform Graphs, International Journal of Contemporary Mathematical Sciences, Volume 5, No. 55, pp.2745-2751, 2010.
[8] F. Harary, Graph Theory, AddisonWesley, Reading Massachusetts, 1969.
[9] Technical Report, DST grant-in-aid project No.SR/S4/MS:277/05, funded by the Department of Science& Technology (DST), April 2011.
Beena Koshy, "CDPU Hypergraphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 150-154, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P520