1 research outputs found

    Uniformly most reliable three-terminal graph of dense graphs

    Full text link
    Suppose that every edge of a graph GG survives independently with a fixed probability between 00 and 11. The three-terminal reliability is the connection probability of the fixed three target vertices r,sr,s and tt in a three-terminal graph. This research focuses on the uniformly most reliable three-terminal graph of dense graphs with nn vertices and mm edges in some ranges. First, we give the locally most reliable three-terminal graphs of nn and mm in a certain range for pp close to 00 and for pp close to 11. And then, we prove that there is no uniformly most reliable three-terminal graph with certain ranges of nn and mm. Finally, some uniformly most reliable graphs are given for (n2)βˆ’2\binom{n}{2}-2 (4≀n≀64\leq n\leq 6) and (n2)βˆ’1\binom{n}{2}-1 (nβ‰₯5n\geq5). This study of uniformly or locally most reliable three-terminal graph provides helpful guidance for constructing highly reliable network structures involving three key vertices as target vertices
    corecore