Read e-book online Topological Structure and Analysis of Interconnection PDF

By Junming Xu

ISBN-10: 1402000200

ISBN-13: 9781402000201

This ebook offers the main uncomplicated difficulties, recommendations, and well-established effects from the topological constitution and research of interconnection networks within the graph-theoretic language. It covers the elemental ideas and strategies of community layout, numerous famous networks reminiscent of hypercubes, de Bruijn digraphs, Kautz digraphs, double loop, and different networks, and the most recent parameters to degree functionality of fault-tolerant networks corresponding to Menger quantity, Rabin quantity, fault-tolerant diameter, wide-diameter, limited connectivity, and (l,w)-dominating quantity. viewers: The ebook is appropriate for these readers who're engaged on or intend to begin study in layout research of the topological constitution of interconnection networks, quite undergraduates and postgraduates focusing on desktop technological know-how and utilized arithmetic.

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Read e-book online Topological Structure and Analysis of Interconnection PDF

This publication offers the main easy difficulties, innovations, and well-established effects from the topological constitution and research of interconnection networks within the graph-theoretic language. It covers the elemental ideas and strategies of community layout, numerous famous networks equivalent to hypercubes, de Bruijn digraphs, Kautz digraphs, double loop, and different networks, and the latest parameters to degree functionality of fault-tolerant networks similar to Menger quantity, Rabin quantity, fault-tolerant diameter, wide-diameter, limited connectivity, and (l,w)-dominating quantity.

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Additional resources for Topological Structure and Analysis of Interconnection Networks (Network Theory and Applications)

Sample text

7. may be s h a r p e n e d t o IN~F ~ IFl

V A n i m p l i e s ~ A, A t ..... A n. (i) ~ A , A t ..... A n implies Proof (i) By iterated application So* of V-inferences we obtain A3 ..... ,A n An (ii) The p r o o f is by induction on cc 1. v A n is not the main f o r m u l a o f t h e l a s t inference, t h e n either A is an a x i o m and s o is A,A t ..... Art or we have t h e p r e m i s e s ~J A j. w A n. But t h e n we have #pJ A j, A 1..... A n by t h e induction h y p o t h e s i s and obtain ~ A , A 1..... A n by the s a m e inference.

Contradiction. 3. Theorem (i) T h e r e i s a l e a s t ordinal w h i c h w i l l b e d e n o t e d b y O. (ii) P o r e v e r y o r d i n a l ~ t h e r e i s a l e a s t o r d i n a l 6 s u c h t h a t ~ < 6. W e c a l l t h i s ordinal t h e s u c c e s s o r of ~ and denote it by ~'. Proof (i) is obvious b e c a u s e o f On*/~. (ii) is an i m m e d i a t e c o n s e q u e n c e o f (O1) and ( 0 2 ) . 4. Lemnla (J) 0t<0t t ( i i ) ~t < ~ c ~ at' < 6' Proof (i) h o l d s by definition. (il) I f ~ < 6, t h e n ~ {[:ct< ~} which implies ~' := min{~: ~ < [ } ~ < 6 ' - F r o m this we obtain by c o n t r a p o s i t i o n ~' ~ 6 ' ~ ~ a6.

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Topological Structure and Analysis of Interconnection Networks (Network Theory and Applications) by Junming Xu


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