3 research outputs found

    ON THE GRUNDY BONDAGE NUMBERS OF GRAPHS

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    For a graph G=(V,E)G=(V,E), a sequence S=(v1,,vk)S=(v_1,\ldots,v_k) of distinct vertices of GG it is called a \emph{dominating sequence} if NG[vi]j=1i1N[vj]N_G[v_i]\setminus \bigcup_{j=1}^{i-1}N[v_j]\neq\varnothing. The maximum length of dominating sequences is denoted by γgr(G)\gamma_{gr}(G). We define the Grundy bondage numbers bgr(G)b_{gr}(G) of a graph GG to be the cardinality of a smallest set EE of edges for which γgr(GE)>γgr(G).\gamma_{gr}(G-E)>\gamma_{gr}(G). In this paper the exact values of bgr(G)b_{gr}(G) are determined for several classes of graphs
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