An Algorithm for Vertex-pair Connectivity

An algorithm for the shortest pairs of arc-disjoint paths problem

“…The processes for finding the shortest pair of arc-disjoint between 2 v and 1 v . The solution contains two paths: 2 1 v v and…”

“…In 1967, Frisch firstly gave algorithms for the question [2] and later Steiglitz and Bruno revised Frisch's algorithms [3], but all of them didn't involve how to make the total length be shortest. In 1969, Takamori treated the problem of finding two arc-disjoint paths with maximum total capacity [4].…”

A new planarity test based on 3-connectivity

“…The set m(G) is given by vz, ~31, (~1, v3,v41, 1~2, v3, ~4, {vi, vz, v,)l. It would seem that the set of meshes of G depends on the plane representation of G, but the fact is that if G is a planar, simple, triply connected graph, then m(G) is independent of the plane representation chosen to calculate the set of meshes. This property of planar, simple, triply connected graphs follows from the work of Whitney [2], [3] and is also enunciated in a paper by Mac Lane [4].…”

A matrix decomposition-reduction procedure for the pole-zero calculation of transfer functions

“…where := means that, for all s, the two sides are equal to within a con stant multiplier. Once det U is transformed into the form of (16), eigenvalues of U together with I superfluous zeros constitute the so lutions of (14) . This paper is not concerned with how the eigenvalues of a matrix are calculated.…”

“…To find a path, which does not pass through the grounded node, is a very simple task. In the general case, a pair of node-disjoint paths can be found using, for example, the algorithm pre sented by Frisch [14].…”