Maryam Moosavi Majd, Hamid R. Maimani, Abolfazl Tehranian

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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.


Grundy Domination Number,Grundy Bondage Number.

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bibitem{B1} {sc B. Brev{s}ar, Cs. Bujt´as, T. Gologranc, S. Klav¡zar, G. Ko¡smrlj, B. Patk´os, Z. Tuza {rm and} M. Vizer}:

{it Grundy dominating sequences and zero forcing sets}, Discrete Optim., {bf 26} (2017), 66-77.

bibitem{BBGKK} {sc B. Brev{s}ar, C. Bujtas, T. Gologranc, S. Klavzar, G. Kosmrlj, B. Patkos, Z. Tuza {rm and} M. Vizer}: {it Dominating sequences in grid-like and toroidal graphs}, Electron. J. Combin., {bf 23} (2016), P4.34 (19 pages).

bibitem{BGK} {sc B. Brev{s}ar, T. Gologranc {rm and} T. Kos}: {it Dominating sequences under atomic changes with applications in Sierpinski and interval graphs}, Appl. Anal. Discrete Math., {bf 10} (2016), 518-531.

bibitem{BKT} {sc B. Brev{s}ar, Kos {rm and} Terros}: {it Grundy domination and zero forcing in Kneser graphs}, Ars Math. Contemp., {bf 17} (2019), 419-430.

bibitem{BGMRR} {sc B. Brev{s}ar, T. Gologranc, M. Milaniv{c}, D. F. Rall {rm and} R. Rizzi}: {it Dominating sequences in graphs}, Discrete Math., {bf 336} (2014), 22-36.

bibitem{BHR} {sc B. Brev{s}ar, M. A. Henning {rm and} D. F. Rall}: {it Total dominating sequences in graphs}, Discrete Math., {bf 339} (2016) 1165-1676.

bibitem{BKNT} {sc B. Brev{s}ar, T. Kos, G. Nasini {rm and} P. Torres}: {it Total dominating sequences in trees, split graphs, and under modular decomposition}, Discrete Optim., {bf 28} (2018), 16-30.

bibitem{CL} {sc G. Chartrand {rm and} L. Lesniak}: {it Graphs and digraphs}, Third Edition, CRC Press,(1996).

bibitem{HHS} {sc T. W. Haynes, S. Hedetniemi {rm and} P. Slater}: {it Fundamentals of Domination in Graphs}, CRC Press, (1998).

bibitem{HY} {sc M. A. Henning {rm and} A. Yeo}: {it Total domination in graphs}, (Springer Monographs in Mathematics.) ISBN-13: 987-1461465249 (2013).

bibitem {MM} {sc S. M. Moosavi Majd {rm and} H. R. Maimani}: {it Grundy domination sequences in generalized corona products of graphs}, Facta Universitatis Ser: Math. Inform., Vol. {bf 35}, No 4 (2020) 1231--1237.

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


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