Embedding And Structure Connectivity Of Complete Transposition Graph

Except the first introductory chapter,the rest of the paper mainly investigate the embedded connectivity,struture connectivity and substructure connectivity of complete transposition graph.It is well known that the connectivity、(G)and edge-connectivity λ(G)of a network G are two important measures for fault tolerance of a network.For an n-dimensional recursive interconnection network Gn,the h-embedded connectivity of Gn,denoted by ζh(Gn)(resp.the h-embedded edge-connectivity of Gn,denoted by ηh(Gn)),is the cardinality of a minimum subset of vertices(resp.edges),if any,whose deletion disconnects Gn and each vertex of remaining com-ponents is contained in an undamaged-dimensional subnetwork Gh.Chapter 2 investigate the h-embedded connectivity and h-embedded edge-connectivity of complete-transposition graph.The following results has been proved:ζh(CTn)=(?)[(n(n-1)-h(h-1)]where 2≤h≤n-2,ηh(CTn)=(?)[n(n-1)-h(h-1)]where 2≤h≤n—1.Let T be a certain particular connected subgraph of G.The T-Structure connec-tivity k(G;T)(T-Substrncture connectivity Ks(G;T),respectively)of graph G,is the minimum number of set of subgraphs F= {T′1,T′2...,T′m｝(F=｛T1,T2,...,Tm},respectively)in G,such that every T′i’≌T(Ti∈F is a connected subgraph of T,respectively)for every 1≤i<≤m and F’s removal will disconnected G.In Chap-ter 3 investigate the structure connectivity k(G;T)and substructure connectivity Ks(G;T)of complete-transposition graph.The following results has been proved,n≥4,And,...