<p>A property ℘ is defined to be a nonempty isomorphism-closed subclass of the class all finite simple graphs. A set <em>S</em> vertices graph <em>G</em> said ℘-set if <em>G</em>[<em>S</em>]∈ ℘. The maximum and minimum cardinalities are denoted by <em>M</em><sub>℘</sub>(<em>G</em>) <em>m</em>&l...

Given a topology of local parity-check constraints, a maximally recoverable code (MRC) can correct all erasure patterns that are information-theoretically correctable. In a grid-like topology, there are a local constraints in every column forming a column code, b local constraints in every row forming a row code, and h global constraints in an (m × n) grid of codeword. Recently, Gopalan et al. ...

We study the cross product as a method for generating and analyzing interconnection network topologies for multiprocessor systems. Consider two interconnection graphs G1 and G2 each with some established properties such as symmetry, low degree and diameter, scalability, simple optimal routing, recursive structure (partitionability), fault tolerance, existence of nodedisjoint paths, low cost emb...

This paper focuses on a generalized two-layer network and its synchronizability, which randomly generate different topologies at each layer. kind of can better describe some irregular networks in reality. From the master stability function method synchronization analysis, we estimate largest eigenvalue lowest nonzero supra-Laplacian matrix. Then, influence node coupling strength synchronizabili...

In this paper, we present a new extension of the butterfly digraph, which is known as one of the topologies used for interconnection networks. The butterfly digraph was previously generalized from binary to d-ary. We define a new digraph by adding a signed label to each vertex of the d-ary butterfly digraph. We call this digraph the dihedral butterfly digraph and study its properties. Furthermo...