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Graphs with the smallest number of minimum cut sets

✍ Scribed by Derek Smith


Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
630 KB
Volume
14
Category
Article
ISSN
0028-3045

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πŸ“œ SIMILAR VOLUMES


The number of cut-vertices in a graph of
✍ Michael O. Albertson; David M. Berman πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 228 KB

Albertson, M.O. and D.M. Berman, The number of cut-vertices in a graph of given minimum degree, Discrete Mathematics 89 (1991) 97-100. A graph with n vertices and minimum degree k 2 2 can contain no more than (2k -2)n/(kz -2) cut-vertices. This bound is asymptotically tight. \* Research supported in

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Topp, J., Graphs with unique minimum edge dominating sets and graphs with unique maximum independent sets of vertices, Discrete Mathematics 12 1 (1993) 199-210. A set I of vertices of a graph G is an independent set if no two vertices of I are adjacent. A set M of edges of G is an edge dominating s

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The maximum number of cutvertices in a connected graph of order n having minimum degree at least 6 is determined for 6 > 5.

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This note presents a solution to the following problem posed by Chen, Schelp, and SoltΓ©s: find a simple graph with the least number of vertices for which only the degrees of the vertices that appear an odd number of times are given.

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✍ ZoltΓ‘n FΓΌredi πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 286 KB πŸ‘ 2 views

Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,