m-ETERNAL TOTAL BONDAGE NUMBER IN CIRCULANT GRAPHS

An Eternal dominating set of a graph is defined as a set of guards located at vertices, required to protect the vertices of the graph against infinitely long sequences of attacks, such that the configuration of guards induces a dominating set at all times. The eternal m-security number is defined as the minimum number of guards to handle an arbitrary sequence of single attacks using multiple-guard shifts. Klostermeyer and Mynhardt defined the m-eternal total domination number of a graph G denoted by gamma(infinity)(mt)(G) as the minimum number of guards to handle an arbitrary sequence of single attacks using multiple guard shifts and the configuration of guards always induces a total dominating set. We define the m-Eternal Total bondage number of a graph G denoted by bmt(G) as the minimum cardinality of set of edges E ' subset of E(G) for which gamma(infinity)(mt)(G - E ') > gamma(infinity)(mt)(G) and G - E ' does not contain isolated vertices. In this paper we find the exact values of bmt(G) for Circulant graphs C(n()1, 2) and C-n(1, 3).