The total bondage number of grid graphs

Authors:
Fu-Tao Hu;You Lu;Jun-Ming Xu
Affiliations:
School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an Shaanxi, 710072, China;School of Mathematical Sciences, University of Science and Technology of China, Wentsun Wu Key Laboratory of CAS, Hefei, Anhui, 230026, China
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

The total domination number of a graph G without isolated vertices is the minimum number of vertices that dominate all vertices in G. The total bondage number b"t(G) of G is the minimum number of edges whose removal enlarges the total domination number. This paper considers grid graphs. An (n,m)-grid graph G"n","m is defined as the cartesian product of two paths P"n and P"m. This paper determines the exact values of b"t(G"n","2) and b"t(G"n","3), and establishes some upper bounds of b"t(G"n","4).