Bondage number of strong product of two paths

作者：Zhao, Weisheng; Zhang, Heping^*

来源：Frontiers of Mathematics in China, 2015, 10(2): 435-460.

DOI：10.1007/s11464-014-0391-5

• Bondage number
• strong product
• path

The bondage number b(G) of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of the bondage number of the strong product of two paths. That is, for any two positive integers m a (c) 3/4 2 and n a (c) 3/4 2, b(P (m) aS P (n) ) = 7 - r(m) - r(n) if (r(m), r(n)) = (1, 1) or (3, 3), 6 - r(m) - r(n) otherwise, where r(t) is a function of positive integer t, defined as r(t) = 1 if t a parts per thousand 1 (mod 3), r(t) = 2 if t a parts per thousand 2 (mod 3), and r(t) = 3 if t a parts per thousand 0 (mod 3).

• 出版日期2015-4
• 单位兰州大学