Random walks on graphs have turned out to be a powerful tool in the design of algorithms and other applications. In particular, expander graphs, which are graphs on which random walks have particularly good properties, are extremely useful in complexity and other areas of computer science. In this chapter we will study random walks on general graphs, leading to a the randomized logspace algorit...

For n ∈ N and D ⊆ N, the distance graph P n has vertex set {0, 1, . . . , n− 1} and edge set {ij | 0 ≤ i, j ≤ n − 1, |j − i| ∈ D}. The class of distance graphs generalizes the important and very well-studied class of circulant graphs which have been proposed for numerous network applications. In view of fault tolerance and delay issues in these applications, the connectivity and diameter of cir...

The g-good-neighbor connectivity of G is a generalization the concept connectivity, which just for, and an important parameter in measuring fault tolerance reliability interconnection network. Many well-known networks can be constructed by Cartesian products some simple graphs. In this paper, we determine product We give exact value two complete graphs for , mesh cylindrical grid torus .

Short cycles connectivity is a generalization of ordinary connectivity. Instead by a path (sequence of edges), two vertices have to be connected by a sequence of short cycles, in which two adjacent cycles have at least one common vertex. If all adjacent cycles in the sequence share at least one edge, we talk about edge short cycles connectivity. It is shown that the short cycles connectivity is...

This paper is devoted to calculations of connectivity probabilities and distributions of connectivity components numbers in planar and recursively defined and parallel-sequential random graphs. These calculations are based on asymptotic formulas for connectivity probabilities and on recurrent relations for different deterministic and stochastic characteristics of random graphs and on limit theo...

Extra edge connectivity and diagnosability have been employed to investigate the fault tolerance properties of network structures. The p-extra ?p(?) a graph ? was introduced by Fàbrega Fiol in 1996. In this paper, we find exact values some special graphs. Moreover, give upper lower bounds for ?p(?), graphs with ?p(?)=1,2,n2n2?1,n2n2 are characterized. Finally, obtain three extremal results conn...

1 Abstract Dynamic networks have recently emerged as an efficient way to model various forms of interaction within teams of mobile agents, such as sensing and communication. This article focuses on the use of graphs as models of wireless communications. In this context, graphs have been used widely in the study of robotic and sensor networks and have provided an invaluable modeling framework to...

This paper is concerned with connectivity of graphs associated with generalized knight's moves. The minimal connected generalized knight's graphs are shown to be planar or toroidal, which was unexpected in view of the complex nature of the graph generated by knight's moves on a chess-board. Each move of a knight in chess takes the knight two steps parallel to one side of the board and one step ...

Dynamic networks are characterized by topologies that varywith time and are represented by time-graphs. The notion of connectivity in time-graphs is fundamentally different from that in static graphs. End-to-end connectivity is achieved opportunistically by the store–carry-forward paradigm if the network is so sparse that source–destination pairs are usually not connected by complete paths. In ...