Uniformly Most Reliable Three-Terminal Graph of Dense Graphs

Xie Sun; Zhao Haixing; Yin Jun

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Uniformly Most Reliable Three-Terminal Graph of Dense Graphs

机译：Uniformly Most Reliable Three-Terminal Graph of Dense Graphs

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A graph G with k specified target vertices in vertex set is a k-terminal graph..ek-terminal reliability is the connection probability of the fixed k target vertices in a k-terminal graph when every edge of this graph survives independently with probability p. For the class of two-terminal graphs with a large number of edges, Betrand, Goff, Graves, and Sun constructed a locally most reliable two-terminal graph for p close to 1 and illustrated by a counterexample that this locally most reliable graph is not the uniformly most reliable two-terminal graph. At the same time, they also determined that there is a uniformly most reliable two-terminal graph in the class obtained by deleting an edge from the complete graph with two target vertices..is article focuses on the uniformly most reliable three-terminal graph of dense graphs with n vertices and m edges. First, we give the locally most reliable three-terminal graphs of n and m in certain ranges for p close to 0 and 1..en, it is proved that there is no uniformly most reliable three-terminal graph with specific n and m, where n = 7 and ((n) (2)) - [(n - 3)/2] m ((n) (2)) - 2. Finally, some uniformly most reliable graphs are given for n vertices and m edges, where 4 = n = 6 and m = ((n) (2)) - 2 or n = 5 and m = ((n) (2)) - 1.

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2021年第18期|6664959.1-6664959.10|共10页
作者
Xie Sun; Zhao Haixing; Yin Jun;
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作者单位

Qinghai Normal Univ, Coll Comp, Xining 810008, Peoples R China|Minist Educ, Key Lab Tibetan Informat Proc, Xining 810008, Peoples R China|Key Lab Tibetan Informat Proc & Machine Translat, Xining 810008, Peoples R China|Qinghai Univ, Teaching & Res Dept Ba;

Qinghai Normal Univ, Coll Comp, Xining 810008, Peoples R China|Minist Educ, Key Lab Tibetan Informat Proc, Xining 810008, Peoples R China|Key Lab Tibetan Informat Proc & Machine Translat, Xining 810008, Peoples R China|State Key Lab Tibetan Intelligent In;

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Uniformly Most Reliable Three-Terminal Graph of Dense Graphs

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