Further Results on the Hop Domination Number of a Graph

被引:1
|
作者
Anusha, D. [1 ]
Robin, S. Joseph [2 ]
John, J. [3 ]
机构
[1] Sree Devi Kumari Womens Coll, Dept Math, Kuzhithurai 629163, India
[2] Scott Christian Coll, Dept Math, Nagercoil 629003, India
[3] Govt Coll Engn, Dept Math, Tirunelveli 627007, India
关键词
Distance; hop domination; hop domination number; upper hop domination number; NP-complete;
D O I
10.5269/bspm.63022
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A hop dominating set S in a connected graph G is called a minimal hop dominating set if no proper subset of S is a hop dominating set of G. The upper hop domination number gamma(+)(h) (G) of G is the maximum cardinality of a minimal hop dominating set of G. Some general properties satisfied by this concept are studied. It is shown that for every two positive integers a and b where 2 <= a <= b, there exists a connected graph G such that gamma(h)(G) = a and gamma(+)(h) (G) = b. It is proved that minimal hop dominating set is NP-complete. It is proved that gamma(h)(G) and gamma(G) are in general incomparable. It is shown that for every pair of positive integers a and b with a >= 2 and b >= 1, there exists a connected graph G such that gamma(h)(G) = a and gamma(G) = b. We present an algorithm to compute minimal hop dominating set of G. Finally, we formulate an Integer linear programming problem to compute the hop domination number of G.
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页数:12
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