Abstract
AbstractThis paper characterizes a class 𝒢 of partial 4‐trees in terms of a set of seven forbidden minors. The class 𝒢 contains several known classes of graphs, including both Δ ‐ Y and Y ‐ Δ graphs. A set of six graph reduction operations is defined, and it is shown that a graph G ∈ 𝒢 iff G can be reduced to an edgeless graph by a finite sequence of these operations. The all‐terminal reliability R(G) of a graph G is the probability that G is connected. The characterization of 𝒢 is used to develop an O(n log n) algorithm to compute R(G) for all n‐point graphs in 𝒢. The running time is O(n) for planar graphs in 𝒢.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
