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| Paper IPM / M / 17632 |
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| Abstract: | |
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Let G be a finite simple non-complete connected graph on {1, . . . , n}
and κ(G) ⥠1 its vertex connectivity. Let f(G) denote the number of free vertices
of G and diam(G) the diameter of G. Being motivated by the computation of
the depth of the binomial edge ideal of G, the possible sequences (n, q, f, d) of
integers for which there is a finite simple non-complete connected graph G on
{1, . . . , n} with q = κ(G), f = f(G), d = diam(G) satisfying f + d = n + 2 â q will
be determined. Furthermore, finite simple non-complete connected graphs G on
{1, . . . , n} satisfying f(G) + diam(G) = n + 2 â κ(G) will be classified.
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