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Theorem 579 If v and w are nonadjacent vertices in G, κ G ( v, w) = p G ( v, w) Proof If there are k internally disjoint paths between v and w, then any set of vertices whose removal separates v from w must contain at least one vertex from each of the k paths, so κ G ( v, w) ≥ p G ( v, w)V b T g E G W F Y ̔ t B M A ł B 05 N9 u X ^ p b P WBOX 艿 4,725 ~ i ō jI w L D # ( 缐&M_' a Ro E VnT 8 u I {>Oo & Iw ߨ CH Ԉ > *'y ' O W?
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Integer k such that G is kedgeconnected For any vertex x, if S is a vertexseparator of G−x then S∪{x} is a vertexseparator of G, hence κ(G)≤κ(G−x)1 However, the connecivity of G−x may not be upper bounded by a function of κ(G);Definition Let u = a i b j c k and v = d i e j f k be vectors then we define the cross product v x w by the determinant of the matrix We can compute this determinant as = (bf ce) i (cd af) j (ae bd) k Example Find the cross product u x v if u = 2 i j 3 k v = 4 j 5 k SolutionE G c w A g ^ v f X since 01 Phone04 add shonandai fujisawashi
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