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- W2929992297 abstract "A set of vertices $S$ of a connected graph $G$ is a nonseparating independent set if $S$ is independent and $G-S$ is connected. The nsis number $mathcal{Z}(G)$ is the maximum cardinality of a nonseparating independent set of $G$. It is well known that computing the nsis number of graphs is NP-hard even when restricted to $4$-regular graphs. In this paper, we first present a new sufficient and necessary condition to describe the nsis number. Then, we completely solve the problem of counting the nsis number of hypercubes $Q_{n}$ and Cartesian product of two cycles $C_{m} square C_{n}$, respectively. We show that $mathcal{Z}(Q_{n}) = 2^{n-2}$ for $n geq 2$, and $mathcal{Z}(C_{m} square C_{n}) = n + lfloor (n+2)/4 rfloor$ if $m = 4$, $m + lfloor (m+2)/4 rfloor$ if $n = 4$ and $lfloor mn/3 rfloor$ otherwise. Moreover, we find a maximum nonseparating independent set of $Q_{n}$ and $C_{m} square C_{n}$, respectively." @default.
- W2929992297 created "2019-04-11" @default.
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- W2929992297 date "2020-02-01" @default.
- W2929992297 modified "2023-09-25" @default.
- W2929992297 title "Nonseparating Independent Sets of Cartesian Product Graphs" @default.
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- W2929992297 doi "https://doi.org/10.11650/tjm/190303" @default.
- W2929992297 hasPublicationYear "2020" @default.
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