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- W2023261385 abstract "Let $kappa(G)$ be the connectivity of $G$. The Kronecker product $G_1times G_2$ of graphs $G_1$ and $G_2$ has vertex set $V(G_1times G_2)=V(G_1)times V(G_2)$ and edge set $E(G_1times G_2)={(u_1,v_1)(u_2,v_2):u_1u_2in E(G_1),v_1v_2in E(G_2)}$. In this paper, we prove that $kappa(Gtimes K_2)=textup{min}{2kappa(G), textup{min}{|X|+2|Y|}}$, where the second minimum is taken over all disjoint sets $X,Ysubseteq V(G)$ satisfying (1)$G-(Xcup Y)$ has a bipartite component $C$, and (2) $G[V(C)cup {x}]$ is also bipartite for each $xin X$." @default.
- W2023261385 created "2016-06-24" @default.
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- W2023261385 date "2011-06-07" @default.
- W2023261385 modified "2023-09-24" @default.
- W2023261385 title "Connectivity of Kronecker products by K2" @default.
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- W2023261385 doi "https://doi.org/10.48550/arxiv.1106.1255" @default.
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