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Periodic Graphs
, 2008
"... Let X be a graph on n vertices with with adjacency matrix A and let H(t) denote the matrixvalued function exp(iAt). If u and v are distinct vertices in X, we say perfect state transfer from u to v occurs if there is a time τ such that H(τ)u,v  = 1. If u ∈ V (X) and there is a time σ such that H ..."
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Cited by 9 (3 self)
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such that H(σ)u,u  = 1, we say X is periodic at u with period σ. We show that if perfect state transfer from u to v occurs at time τ, then X is periodic at both u and v with period 2τ. We extend previous work by showing that a regular graph with at least four distinct eigenvalues is periodic with respect
ωPeriodic graphs
, 2008
"... ωperiodic graphs are introduced and studied. These are graphs which arise as the limits of periodic extensions of the nearest neighbor graph on the integers. We observe that all bounded degree ωperiodic graphs are ameanable. We also provide examples of ωperiodic graphs which have exponential volu ..."
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Cited by 4 (0 self)
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ωperiodic graphs are introduced and studied. These are graphs which arise as the limits of periodic extensions of the nearest neighbor graph on the integers. We observe that all bounded degree ωperiodic graphs are ameanable. We also provide examples of ωperiodic graphs which have exponential
ωPeriodic graphs
"... ωPeriodic graphs are introduced and studied. These are graphs which arise as the limits of periodic extensions of the nearest neighbor graph on the integers. We observe that all bounded degree ωperiodic graphs are amenable. We also provide examples of ωperiodic graphs which have exponential volum ..."
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ωPeriodic graphs are introduced and studied. These are graphs which arise as the limits of periodic extensions of the nearest neighbor graph on the integers. We observe that all bounded degree ωperiodic graphs are amenable. We also provide examples of ωperiodic graphs which have exponential
Topological Labeling of Periodic Graphs
, 1998
"... In this paper, we extend the definition of topological labeling of nite directed acyclic graphs to infinite acyclic periodic graphs. Unlike finite acyclic graphs, we show that acyclic periodic graphs cannot be topologically labelled with integers in general. However, we show that these graphs can be ..."
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In this paper, we extend the definition of topological labeling of nite directed acyclic graphs to infinite acyclic periodic graphs. Unlike finite acyclic graphs, we show that acyclic periodic graphs cannot be topologically labelled with integers in general. However, we show that these graphs can
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
PolynomialTime Analysis of Toroidal Periodic Graphs
, 2000
"... A toroidal periodic graph G^D is defined by an integral... ..."
microelectronics, of Free Schedule in Periodic Graphs
"... In this paper we address a scheduling problem for regular algorithms which can be described using aperiodic graph. The free schedule of those regular iterative algorithms is analyzed in a conelike index space. Since the determination of a free schedule is closely related to the longest path probl ..."
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problem, the structure of longest paths in periodic graphs must be determined. It will be shown that free schedules also have some kind of regularity. We also present algorithms for calculating this structure and give an estimate on the computational complexity of our algorithms. Finally, it is proven
Results 1  10
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673,786