On independent position sets in graphs
Abstract An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, w...
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Universidad Católica del Norte, Departamento de Matemáticas
2021
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oai:scielo:S0716-091720210002003852021-04-03On independent position sets in graphsThomas,Elias JohnChandran S. V.,Ullas General position set Independent set Independent number Independent position number Abstract An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariants.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.2 20212021-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000200385en10.22199/issn.0717-6279-2021-02-0023 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
General position set Independent set Independent number Independent position number |
| spellingShingle |
General position set Independent set Independent number Independent position number Thomas,Elias John Chandran S. V.,Ullas On independent position sets in graphs |
| description |
Abstract An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariants. |
| author |
Thomas,Elias John Chandran S. V.,Ullas |
| author_facet |
Thomas,Elias John Chandran S. V.,Ullas |
| author_sort |
Thomas,Elias John |
| title |
On independent position sets in graphs |
| title_short |
On independent position sets in graphs |
| title_full |
On independent position sets in graphs |
| title_fullStr |
On independent position sets in graphs |
| title_full_unstemmed |
On independent position sets in graphs |
| title_sort |
on independent position sets in graphs |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2021 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000200385 |
| work_keys_str_mv |
AT thomaseliasjohn onindependentpositionsetsingraphs AT chandransvullas onindependentpositionsetsingraphs |
| _version_ |
1718439897740607488 |