论文标题
$ g $ -Extra Edge-Connectivation falanced Hypercubes
The $g$-extra edge-connectivity of balanced hypercubes
论文作者
论文摘要
$ g $ -Extra边缘连接性是互连网络可靠性的重要措施。最近，Yang等人。 [应用。数学。计算。 320（2018）464--473]确定了$ 3 $ -Extra Edge-connectitive $ bh_n $的$ 3 $ -EXTRA边缘连接性，并推测$ g $ -G $ -EXTRA EDGE-Connectitive $ bh_n $ is $ bh_n $ is $λ_g（bh_n）= 2（bh_n）= 2（G+1）在本文中，我们确认了他们的猜想，以$ n \ geq 6- \ dfrac {12} {g+1} $和$ 2 \ leq g \ leq 8 $，并将其猜想解释为$ n \ geq \ geq \ dfrac {3e_g（bh_n）} $和$ 9 $ s $ s $ s $ s $ $ e_g（bh_n）= \ max \ {| e（bh_n [u]）| \ mid u \ subseteq v（bh_n），| u | = g+1 \} $。
The $g$-extra edge-connectivity is an important measure for the reliability of interconnection networks. Recently, Yang et al. [Appl. Math. Comput. 320 (2018) 464--473] determined the $3$-extra edge-connectivity of balanced hypercubes $BH_n$ and conjectured that the $g$-extra edge-connectivity of $BH_n$ is $λ_g(BH_n)=2(g+1)n-4g+4$ for $2\leq g\leq 2n-1$. In this paper, we confirm their conjecture for $n\geq 6-\dfrac{12}{g+1}$ and $2\leq g\leq 8$, and disprove their conjecture for $n\geq \dfrac{3e_g(BH_n)}{g+1}$ and $9\leq g\leq 2n-1$, where $e_g(BH_n)=\max\{|E(BH_n[U])|\mid U\subseteq V(BH_n), |U|=g+1\}$.
