PBIB-DESIGNS AND ASSOCIATION SCHEMES FROM MINIMUM SPLIT DOMINATING SETS OF CERTAIN JUMP SIZES OF CIRCULANT GRAPHS

Print ISSN: 0972-7752 | Online ISSN: | Total Downloads : 109

Volume : 14 , Issue : 1
DOI:
Author :
V. R. Kulli (Department of Mathematics, Gulbarga University, Gulbarga-585106, INDIA)
B. Chaluvaraju (Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bengaluru -560 056, INDIA.)
M. Kumara (Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bengaluru -560 056, INDIA.)

Abstract

A dominating set D of a graph G = (V, E) is a split dominating set if the induced subgraph ⟨V-D⟩ is disconnected. The split domination number γs(G) is the minimum cardinality of a split dominating set of G. The set of vertices is a γs- set if it is split dominating set with γs(G). In this paper, we obtain the total number of γs-sets, the Partially Balanced Incomplete Block (PBIB)-Designs on γs-sets of certain jump sizes of Circulant graphs with m-association schemes for 1≤ m≤⌊ p/2⌋.

Keywords and Phrases

Association schemes; PBIB Designs; Split Dominating sets; Circulant graph.

A.M.S. subject classification

05C51, 05E30, 05C69.

.....

Download PDF 109 Click here to Subscribe now