The nonsplit domination in subdivision graph
Abstract A dominating set D of a graph G = (V, E) is a nonsplit dominating set if the induced subgraph 〈V − D〉 is connected. The nonsplit domination number γ ns (G) of G is the minimum cardinality of a nonsplit dominating set. An edge e = uv of a graph G is sa...
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Universidad Católica del Norte, Departamento de Matemáticas
2020
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oai:scielo:S0716-091720200005011132020-11-16The nonsplit domination in subdivision graphChrislight,R. JemimalSunitha Mary,Y. Therese Domination number Nonsplit domination number Subdivision graph Nonsplit domination number of subdivision graph Abstract A dominating set D of a graph G = (V, E) is a nonsplit dominating set if the induced subgraph 〈V − D〉 is connected. The nonsplit domination number γ ns (G) of G is the minimum cardinality of a nonsplit dominating set. An edge e = uv of a graph G is said to be subdivided if e is replaced by the edges uw and vw for some vertex w not in V (G). The graph obtained from G by subdividing each edge of G exactly once is called the subdivision graph of G and is denoted by S(G). In this paper, we study the nonsplit domination number of subdivision graph. We determine exact values of the nonsplit domination number of subdivision graph for some standard graphs. We also obtain bounds and relationship with other graph theoretic parameters for the γ ns (S(G)).info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.5 20202020-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501113en10.22199/issn.0717-6279-2020-05-0068 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Domination number Nonsplit domination number Subdivision graph Nonsplit domination number of subdivision graph |
| spellingShingle |
Domination number Nonsplit domination number Subdivision graph Nonsplit domination number of subdivision graph Chrislight,R. Jemimal Sunitha Mary,Y. Therese The nonsplit domination in subdivision graph |
| description |
Abstract A dominating set D of a graph G = (V, E) is a nonsplit dominating set if the induced subgraph 〈V − D〉 is connected. The nonsplit domination number γ ns (G) of G is the minimum cardinality of a nonsplit dominating set. An edge e = uv of a graph G is said to be subdivided if e is replaced by the edges uw and vw for some vertex w not in V (G). The graph obtained from G by subdividing each edge of G exactly once is called the subdivision graph of G and is denoted by S(G). In this paper, we study the nonsplit domination number of subdivision graph. We determine exact values of the nonsplit domination number of subdivision graph for some standard graphs. We also obtain bounds and relationship with other graph theoretic parameters for the γ ns (S(G)). |
| author |
Chrislight,R. Jemimal Sunitha Mary,Y. Therese |
| author_facet |
Chrislight,R. Jemimal Sunitha Mary,Y. Therese |
| author_sort |
Chrislight,R. Jemimal |
| title |
The nonsplit domination in subdivision graph |
| title_short |
The nonsplit domination in subdivision graph |
| title_full |
The nonsplit domination in subdivision graph |
| title_fullStr |
The nonsplit domination in subdivision graph |
| title_full_unstemmed |
The nonsplit domination in subdivision graph |
| title_sort |
nonsplit domination in subdivision graph |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2020 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501113 |
| work_keys_str_mv |
AT chrislightrjemimal thenonsplitdominationinsubdivisiongraph AT sunithamaryytherese thenonsplitdominationinsubdivisiongraph AT chrislightrjemimal nonsplitdominationinsubdivisiongraph AT sunithamaryytherese nonsplitdominationinsubdivisiongraph |
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1718439881312567296 |