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Applied Mathematical Sciences
Article . 2015 . Peer-reviewed
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On connected closed geodetic number of the join of graphs

Authors: Mercedita A. Langamin; Michael E. Subido; Imelda S. Aniversario;

On connected closed geodetic number of the join of graphs

Abstract

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

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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).
BIP!Citations provided by BIP!
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.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Top 10%
Average
gold