Discrete Mathematics with Graph Theory (3rd Edition) 253

# Discrete Mathematics with Graph Theory (3rd Edition) 253 -...

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Section 9.2 (b) iv. [BB] Joining V2 and V6 gives eight edges and still six vertices. 1. ii. New beta index = ~ = 1.3. New accessibility indices are 4, 2.3, 2.3, 4, 9, 1. City V6 is most accessible; V5 is least accessible. VI V2 V3 V4 V5 V6 V7 VI 0 1 2 2 2 3 3 V2 1 0 1 1 1 2 2 V3 2 1 0 2 2 3 3 V4 2 1 2 0 2 1 2 V5 2 1 2 2 0 2 1 V6 3 2 3 1 2 0 1 V7 3 2 3 2 1 1 0 vertex VI V2 V3 V4 V5 V6 column total 13 8 13 10 10 12 vertex degree 1 4 1 2 2 2 accessibility index 13 2 13 5 5 6 V7 12 2 6 Here, V2 is most accessible; VI and V3 are least accessible. iii. New beta index = ~; New accessibility indices are 6, 2, 6, 5, 5, 6, 6. 251 City V2 is still most accessible; now V6 and V7 are tied with VI and V3 for least accessible. iv. New beta index = ~; New accessibility indices are 12, 1.4, 12, 5, 5, 3, 6. V2 is still most accessible; VI and V3 are least accessible. 10. [BB] Kn has G) = n(n 2 -I) edges. Each of the n vertices has degree n -1, so the sum of the degrees is n(n - 1). This is twice the number of edges, as asserted by Proposition 9.2.5.
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