Abstract Edge connectivity is an important parameter for the reliability of the inter-connection network. A graph $G$ is strong Menger edge-connected ($SM$-$\lambda $ for short) if there exist min$\{\deg _{G}(u),\deg _{G}(v)\}$ edge-disjoint paths between any pair of vertices $u$ and $v$ of $G$. The conditional edge-fault-tolerance strong Menger edge connectivity of $G$, denoted by $sm_{\lambda }^{r}(G)$, is the maximum integer $m$ such that $G-F$ remains $SM$-$\lambda $ for any edge set $F$ with $|F|\leq m$ and $\delta (G-F)\geq r$, where $\delta (G-F)\geq r$ is the minimum degree of $G-F$. Most of the previous papers discussed $sm_{\lambda }^{r}(G)$ in the case of $r\leq 2$. In this paper, we show that $sm_{\lambda }^{r}(FQ_{n})=2^{r}(n-r+1)-(n+1)$ for $1\leq r\leq n-2$, where $n\geq 4$.

Abstract The connectivity is an important measurement for the fault-tolerance of networks. To provide more accurate measures for the fault-tolerance of networks than the connectivity, some generalizations of connectivity have been introduced. Substructure connectivity and structure connectivity are two extended concepts of classical connectivity. As a variant of the popular network hypercube, the Möbius cubes is also a famous interconnection network in parallel and distributed systems. In this article, we calculate $H$-substructure connectivity and $H$-structure connectivity of Möbius cubes when $H$ is isomorphic to $P_{m},C_{m}$ and $K_{1,m}$.

Abstract A bipartite graph is Hamiltonian laceable if any two of its vertices in different partite sets are connected by a Hamiltonian path. A Hamiltonian laceable graph $G$ is called strongly Hamiltonian laceable if any two of its vertices in the same partite set are connected by a path of length $|V(G)|-2$. A Hamiltonian laceable graph $G$ (with two partite sets $V_0, V_1$) is called hyper-Hamiltonian laceable, if for any vertex $v \in V_{i}$ for $i \in \{0,1\}$, there is a Hamiltonian path of $G-\{v\}$ between any two vertices in $V_{1-i}$. In this paper, we focus on the edge-fault-tolerant strongly Hamiltonian laceability and hyper-Hamiltonian laceability on the class of Cayley graphs generated by transposition trees, which are a generalization of star graph and bubble-sort graph. For every $n$-dimensional Cayley graph generated by a transposition tree $\Gamma _n$, we show that $\Gamma _{n}-F$ is strongly Hamiltonian laceable for any $F \subseteq E(\Gamma _{n})$ with $|F|\leq n-3$, which generalizes results in [ 1, 11], and show that $\Gamma _{n}-F$ is hyper-Hamiltonian laceable for any $F \subseteq E(\Gamma _{n})$ with $|F|\leq n-4$.

We present an enhanced error diffusion halftoning algorithm for which the filter weights and the quantizer thresholds vary depending on input pixel value. The weights and thresholds are optimized based on a human visual system model. Based on an analysis of the edge behavior, a tone dependent threshold is designed to reduce edge effects and start-up delay. We also propose an error diffusion system with parallel scan that uses variable weight locations to reduce worms.

We present a clustered minority pixel error diffusion halftoning algorithm for which the quantizer threshold is modified based on the past output and a dot activation map. Dot size, dot shape, and dot distribution are more controllable, compared with other clustered dot halftone algorithms such as R. Levien's algorithm (see IS&T 8th Int. Congress on Advances in Non-Impact Printing Technologies, p.280-2, 1992). This method also effectively reduces structured worm-like artifacts in midtones that occur in Levien's algorithm. The dot distribution is further improved by using different error diffusion weights for different input gray levels.

Screening is a low complexity halftoning algorithm that has been widely used in many applications. However, screen design requires that the stacking property be obeyed. This constraint limits the texture quality at each gray level. We present a look-up-table based halftoning algorithm for which the stacking constraint is not necessarily satisfied; but the binary patterns for individual levels are still correlated. The binary patterns are designed level by level using the direct binary search method. The algorithm improves halftone image quality compared with screening.

Screen design requires that the stacking property be obeyed. This constraint limits the texture quality at each gray level. To improve the texture quality, we introduce a look-up-table based halftoning algorithm for which the stacking constraint is not necessarily satisfied but the binary patterns for individual levels are still correlated. The algorithm improves the halftone image quality compared with screening.