Let G = (V,E) be an input graph. What is $L_{0.v.w}$ in the case where: (i) v = w; (ii) (v,w) is an edge of G; and (iii) v ≠ w and (v,w) is not an edge of G?

a) 0, 0, and $+\infty$

b) 0, $\ell_{v w}$ , and $\ell_{v w}$

c) 0, $\ell_{v w}$ , and $+\infty$

d) $+\infty$ , $\ell_{v w}$ , and $+\infty$

(See Section 18.4.6 for the solution and discussion.)

Question

Let G = (V,E) be an input graph. What is [latex]L_{0.v.w}[/latex] in the case where: (i) v = w; (ii) (v,w) is an edge of G; and (iii) v ≠ w and (v,w) is not an edge of G?

a) 0, 0, and [latex]+\infty[/latex]

b) 0, [latex]\ell_{v w}[/latex] , and [latex]\ell_{v w}[/latex]

c) 0, [latex]\ell_{v w}[/latex] , and [latex]+\infty[/latex]

d) [latex]+\infty[/latex] , [latex]\ell_{v w}[/latex] , and [latex]+\infty[/latex]

(See Section 18.4.6 for the solution and discussion.)

Accepted Answer

Correct answer: (c). If v = w, the only v-w path with no internal vertices is the empty path (with length 0). If (v,w) ∈ E, the only such path is the one-hop path v → w (with length [latex]\ell_{v w}[/latex]). If v ≠ w and (v,w) ∉ E, there are no v-w paths with no internal vertices and [latex]{ L}_{0,v,w}=+\infty.[/latex]

Question 18.6: Let G = (V,E) be an input graph. What is L0,v,w in the case ......

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