Explore BrainMass

Explore BrainMass

    Directed Graphs, Vertices and Distinct Paths

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    6. Recall that R^3={(x,y,z):x,y,z(subset of R)}. Let G(V,E) be a directed graph, in which V= {(x,y,z)-(subset of R^3) :x,y,z(subset of R),-10<=x,y,z<=10}.
    Suppose that for any vertex, v=(x,y,z)--[subset of V], the only edges originating at v are the ones joining v to (x+1,y,z),(x,y+1,z),(x,y,z+1) .
    i.e. any path that originates at v , must begin by moving one unit horizontally to
    (x+1,y,z) or one unit vertically to (x,y+1,z) or one unit across to (x,y,z +1) .

    a) How many distinct paths exist between(-1,2,0) and (1,3,7) ?
    b) How many distinct paths exist between(1,0,5) and (8,1,7) ?

    © BrainMass Inc. brainmass.com March 4, 2021, 6:45 pm ad1c9bdddf
    https://brainmass.com/math/graphs-and-functions/directed-graphs-vertices-distinct-paths-60075

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    6. Recall that . Let G(V,E) be a directed graph, in which . Suppose that for any vertex, v=(x,y,z) , the only edges originating at v are the ones joining v to (x+1,y,z),(x,y+1,z),(x,y,z+1). (i.e. any path that originates at v must begin by moving one unit horizontally to (x+1,y,z) or one unit vertically to (x,y+1,z) or ...

    Solution Summary

    Directed Graphs, Vertices and Distinct Paths are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

    $2.49

    ADVERTISEMENT