A generalized reliability analysis of 3-ary n-cubes

Evaluating the reliability of interconnection networks is crucial. The edge-connectivity is a parameter used to assess reliability. In this paper, we discuss a conditional edge-connectivity called the h-extra g-component edge-connectivity. It combines the extra edge-connectivity and the component edge-connectivity. First, this paper proved that $c \lambda_{3}^{h}\left(Q_{n}^{3}\right)=4 n h-$ $4 e_{h}\left(Q_{n}^{3}\right)-h$ for $1 \leq h \leq \frac{1}{2} \cdot 3^{\left\lceil\frac{h}{2}\right\rceil}, n \geq 3$. Then, the paper given the upper bound of h-extra g-component edge-connectivity of the 3 -ary n-cubes for $g \in\left\{4,3^{c}+1\right\}, 1 \leq c \leq\left\lceil\frac{n}{2}\right\rceil-1, n \geq 3$.