The forcing open monophonic number of a graph
For a connected graph G of order n ≥ 2, and for any mínimum open monophonic set S of G, a subset T of S is called a forcing subset for S if S is the unique minimum open monophonic set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing...
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| Main Authors: | , |
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| Language: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2016
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000100005 |
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| Summary: | For a connected graph G of order n ≥ 2, and for any mínimum open monophonic set S of G, a subset T of S is called a forcing subset for S if S is the unique minimum open monophonic set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing open monophonic number of S, de-noted by f om(S), is the cardinality of a minimum forcing subset of S. The forcing open monophonic number of G, denoted by f om(G), is f om(G) = min(f om(S)), where the minimum is taken over all minimum open monophonic sets in G. The forcing open monophonic numbers of certain standard graphs are determined. It is proved that for every pair a, b of integers with 0 ≤ a ≤ b - 4 and b ≥ 5, there exists a connected graph G such that f om(G) = a and om(G) = b. It is analyzed how the addition of a pendant edge to certain standard graphs affects the forcing open monophonic number. |
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