Show simple item record

The edge-to-edge geodetic domination number of a graph

dc.creatorJohn, J.
dc.creatorSujin Flower, V.
dc.date2021-04-27
dc.identifierhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4057
dc.identifier10.22199/issn.0717-6279-4057
dc.descriptionLet G = (V, E) be a connected graph with at least three vertices. A set S Í E is called an edge-to-edge geodetic dominating set of G if S is both an edge-to-edge geodetic set of G and an edge dominating set of G. The edge-to- edge geodetic domination number ¡gee(G) of G is the minimum cardinality of its edge-to-edge geodetic dominating sets and any edge-to-edge geodetic dominating set of minimum cardinality is said to be a gee- set of G. Some general properties satisfied by this concept are studied. Connected graphs of size m?2 with edge-to-geodetic domination number 2 or m or m-1 are charaterized. We proved that if G is a connected graph of size m ? 3 and G­ is also connected,then 4 ?¡gee(G) + ¡gee(G­) ? 2m -2. Moreover we characterized graphs for which the lower and the upper bounds are sharp. It is shown that, for every pair of positive integers a and b with 2 ?a ? b, there exists a connected graph G with gee(G) = a and ¡gee(G) = b. Also it is shown that, for every pair of positive integers a and b with 2 < a ? b, there exists a connected graph G with ¡e(G) = a and¡ gee(G) = b, where ¡e(G) is the edge domination number of G and gee(G) is the edge-to-edge geodetic number of G.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad Católica del Norte.en-US
dc.relationhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4057/3728
dc.rightsCopyright (c) 2021 J. John, V. Sujin Floweren-US
dc.rightshttp://creativecommons.org/licenses/by/4.0en-US
dc.sourceProyecciones (Antofagasta, On line); Vol. 40 No. 3 (2021); 635-658en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 40 Núm. 3 (2021); 635-658es-ES
dc.source0717-6279
dc.source10.22199/issn.0717-6279-2021-03
dc.subjectEdge-to-edge geodetic domination numberen-US
dc.subjectEdge-to-edge geodetic numberen-US
dc.subjectEdge domination numberen-US
dc.subjectGeodetic numberen-US
dc.subject05C69en-US
dc.subject05C12en-US
dc.titleThe edge-to-edge geodetic domination number of a graphen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typePeer-reviewed Articleen-US
dc.typetexten-US


This item appears in the following Collection(s)

Show simple item record