the edge tenacity of a split graph
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abstract
the edge tenacity te(g) of a graph g is de ned as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected split graph with minimum vertex degree δ(g) we prove that if δ(g)≥|e(g)|/[|v(g)|-1] then its edge-tenacity is |e(g)|/[|v(g)|-1] .
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Journal title:
journal of algorithms and computationجلد ۴۷، شماره ۱، صفحات ۱۱۹-۱۲۵
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