An interconnection network is characterized by its topology, routing and flow control. The topology is a directed graph, where the nodes represent the routing modules and the edges represent the channels. Routing specifies how a packet chooses a path on this graph. Flow control examines the allocation of resources, mainly channels and buffers to a packet as it traverses this path. This paper su...

For a permutation π of the vertex set of a graph G, the graph πG is obtained from two disjoint copies G1 and G2 of G by joining each v in G1 to π(v) in G2. Hence if π = 1, then πG = K2 × G, the prism of G. Clearly, γ(G) ≤ γ(πG) ≤ 2γ(G). We study graphs for which γ(K2 × G) = 2γ(G), those for which γ(πG) = 2γ(G) for at least one permutation π of V (G) and those for which γ(πG) = 2γ(G) for each pe...

The entropy of a graph was first introduced by Rashevsky [1] and Trucco [2] to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of definitions of graph entropy measures and generalized graph entropies. Then we survey the known results about them from the following three respects: inequalities and extremal prop...

We consider the class A of graphs that contain no odd hole, no antihole, and no “prism” (a graph consisting of two disjoint triangles with three disjoint paths between them). We prove that every graph G ∈ A different from a clique has an “even pair” (two vertices that are not joined by a chordless path of odd length), as conjectured by Everett and Reed [see the chapter “Even pairs” in the book ...

We present a technique to tackle the parameterised probabilistic model checking problem for a particular class of randomised distributed systems, which we model as Markov Decision Processes. These systems, termed degenerative, have the property that a model of a system with some communication graph will eventually behave like a model of a system with a reduced graph. We describe an induction sc...

Abstract The complementary prism $$\Gamma {\bar{\Gamma }}$$ Γ ¯ is constructed from the disjoint union of a graph $$ and its complement $${\bar{\Gamma if an edge added between each pair identical vertices in . It generalizes Petersen graph, whic...

An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code, or ID code, in a graph G is called the ID code number of G and is denoted γ(G). In this paper, we give upper and lower bounds for the ID code number of the prism of a graph...