Connected edge monophonic number of a graph
For a connected graph G of order n,a set S of vertices is called an edge monophonic set of G if every edge of G lies on a monophonic path joining some pair of vertices in S, and the edge monophonic number m e(G) is the minimum cardinality of an edge monophonic set. An edge monophonic set S of G is a...
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| Autores principales: | , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2013
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000300002 |
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| Sumario: | For a connected graph G of order n,a set S of vertices is called an edge monophonic set of G if every edge of G lies on a monophonic path joining some pair of vertices in S, and the edge monophonic number m e(G) is the minimum cardinality of an edge monophonic set. An edge monophonic set S of G is a connected edge mono-phonic set if the subgraph induced by S is connected, and the connected edge monophonic number m ce(G) is the minimum cardinality of a connected edge monophonic set of G. Graphs of order n with connected edge monophonic number 2, 3 or n are characterized. It is proved that there is no non-complete graph G of order n > 3 with m e(G) = 3 and m ce(G)= 3. It is shown that for integers k,l and n with 4 < k < l < n, there exists a connected graph G of order n such that m e(G) = k and m ce(G) = l.Also, for integers j,k and l with 4 < j < k < l, there exists a connected graph G such that m e(G)= j,m ce(G)= k and g ce(G) = l,where g ce(G) is the connected edge geodetic number ofa graph G. |
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