ON THE GRUNDY BONDAGE NUMBERS OF GRAPHS

Seyedeh Maryam Moosavi Majd, Hamid R. Maimani, Abolfazl Tehranian

DOI Number
https://doi.org/10.22190/FUMI221010006M
First page
091
Last page
096

Abstract


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

Keywords

Grundy Domination Number,Grundy Bondage Number.

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References


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DOI: https://doi.org/10.22190/FUMI221010006M

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