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

Authors

  • 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.)

Keywords:

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

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⌋.

 

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Published

2023-06-16

Issue

Vol. 14 No. 01 (2018): South East Asian Journal of Mathematics and Mathematical Sciences

Section

Articles