<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=undefined&type=result"></script>');
-->
</script>
This study deals primarily with the connected closed geodetic numbers of the join of two graphs which is a modification of the closed geodetic number of graphs studied by Aniversario in [2], a geodetic closure invariant introduced by Buckley and Harary in [4]. The concept of connected closed geodetic number of a graph G, denoted by ccgn(G) is introduced and some of its properties are investigated. It is proved that, if G is a connected graph with cut–vertices and if S is a connected closed geodetic basis of G, such that w is a cut–vertex of G, then each component of G-w contains an element of S. It is shown that every cut–vertex of a connected graph G belongs to every connected closed geodetic basis of G. Some connected graphs G for which the ccgn is equal to p and 2 are characterized. In this paper, the concept of a 2-path connected closure of S in a graph G, denoted by P c 2 [S]G, is introduced. Likewise, the properties of connected closed geodetic basis of a graph G resulting from the join of connected graphs H and K for which K is a complete graph and of connected graphs H and K for which K is not a complete graph are investigated and the ccgn of G is also determined. This research is funded by CHED-FDP. 4918 Mercedita A. Langamin, Imelda S. Aniversario and Michael E. Subido
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 3 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |