Average Resistance of Toroidal Graphs
نویسندگان
چکیده
منابع مشابه
Average Resistance of Toroidal Graphs
Abstract. The average effective resistance of a graph is a relevant performance index in many applications, including distributed estimation and control of network systems. In this paper, we study how the average resistance depends on the graph topology and specifically on the dimension of the graph. We concentrate on d-dimensional toroidal grids and we exploit the connection between resistance...
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The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...
متن کاملNote on "Average resistance of toroidal graphs" by Rossi, Frasca and Fagnani
In our recent paper W.S. Rossi, P. Frasca and F. Fagnani, “Average resistance of toroidal graphs”, SIAM Journal on Control and Optimization, 53(4):2541–2557, 2015, we studied how the average resistances of d-dimensional toroidal grids depend on the graph topology and on the dimension of the graph. Our results were based on the connection between resistance and Laplacian eigenvalues. In this not...
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the tenacity of a graph g, t(g), is de ned by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we de ne τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...
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The average effective resistance of a graph can be computed as a function of its eigenvalues. Using this formula and focusing on toroidal d-dimensional graphs, we study the role of the network topology and specifically of the graph dimension in determining the resistance. Considering sequences of graphs of increasing size, we study the asymptotical behavior of the effective resistance, proving ...
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2015
ISSN: 0363-0129,1095-7138
DOI: 10.1137/130936117