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- Author or Editor: K. S. Bagga x
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For an (r − 2)-edge-connected graphG (r ≥ 3) for orderp containing at mostk edge cut sets of cardinalityr − 2 and for an integerl with 0 ≤l ≤ ⌊p/2⌋, it is shown that (1) ifp is even, 0 ≤k ≤ r(l + 1) − 1, and
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$$\mathop \sum \limits_{v \in V(G)} |\deg _G v - r|< r(2 + 2l) - 2k$$
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, then the edge independence numberβ
1
(G) is at least (p − 2l)/2, and (2) ifp is odd, The sharpness of these results is discussed.
