Partially balanced incomplete block designs associated with minimum perfect dominating sets of Clebsch graph

International Journal of Applied Mathematics and Computation

D. S. Nandappa¹  U. S. Mahabaleswar³  Vinay Kumar² 

[1] University of Mysore, Karnataka$$;University of Mysore$$;Government First Grade College for Women's, Hassan, Karnataka$$

关键词: Partially balanced incomplete block designs;    Minimum perfect dominating set;    Perfect domination number;    strongly regular graphs;   

DOI  :  10.0000/ijamc.2012.4.1.162

来源: PSIT Kanpur

【 摘 要 】

A dominating set $S$ of a graph $G$ is perfect if each vertex of G is dominated by exactly one vertex in $S$. We study the minimum perfect dominating sets in the Petersen graph and in the Clebsch graph. In this paper we show that every minimum perfect dominating set in the Petersen graph and the Clebsch graph induces $K_{1,3}$ and $C_4$ respectively. Further we establish that these classes of minimum perfect dominating sets of Clebsch graph form Partially Balanced Incomplete Block Designs with the parameters (16, 40, 10, 4, 1, 4).

【 授权许可】

Unknown