This paper introduces a new interconnection network topology called the star-crossed cube (SCQ). The SCQ is observed to be superior to other contemporary networks in terms of various topological parameters such as diameter, cost, average distance, and message traffic density. The various performance metrics of the proposed network, including cost effectiveness and time-cost effectiveness, are f...

The star-connected cycles (SCC) graph was recently proposed as an attractive interconnection network for parallel processing, using a star graph to connect cycles of nodes. This paper presents embeddings of p-dimensional meshes into an n-dimensional SCC graph (1 p n), which have load 1, expansion 1, and dilation ranging from 1 to 3 + 2b(n ? 1)=2c + 2bn=4c (the dilation varies among mesh dimensi...

Let G be a finite graph of order n with an eigenvalue μ of multiplicity k. (Thus the μ-eigenspace of a (0, 1)-adjacency matrix of G has dimension k.) A star complement for μ in G is an induced subgraph G−X of G such that |X| = k and G−X does not have μ as an eigenvalue. An exceptional graph is a connected graph, other than a generalized line graph, whose eigenvalues lie in [−2,∞). We establish ...

Let $R$ be a commutative ring and $mathbb{A}(R)$ be the set of all ideals with non-zero annihilators. Assume that $mathbb{A}^*(R)=mathbb{A}(R)diagdown {0}$ and $mathbb{F}(R)$ denote the set of all finitely generated ideals of $R$. In this paper, we introduce and investigate the {it finitely generated subgraph} of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_F(R)$. It is the (undi...

A multiprocessor system consists of a set of processing units and each of them has its own local memory. The processing units in a multiprocessor system are linked in some topology. What we are interested in is a topology proposed by Akers et al. [2,3], called star graph. An n-dimensional star graph can be represented by S,, = (V,,, E,,), where V,, consists of n! nodes in which each node is ide...

In the Star System problem we are given a set system and asked whether it is realizable by the multi-set of closed neighborhoods of some graph, i.e. given subsets S1, S2, ..., Sn of an n-element set V does there exist a graph G = (V, E) with {N [v] : v ∈ V } = {S1, S2, ..., Sn}? For a fixed graph H the H-free Star System problem is a variant of the Star System problem where it is asked whether ...

In a graph G= (V ,E), a subset F ⊂ V (G) is a feedback vertex set of G if the subgraph induced by V (G) \ F is acyclic. In this paper, we propose an algorithm for finding a small feedback vertex set of a star graph. Indeed, our algorithm can derive an upper bound to the size of the feedback vertex set for star graphs. Also by applying the properties of regular graphs, a lower bound can easily b...