## Weakly Connected Closed Geodetic Numbers of the Corona and Composition of Some Graphs

Author:
RACHEL M. PATANGAN1, IMELDA S. ANIVERSARIO* and ROSALIO G. ARTES, JR.
Affiliation:

Department of Mathematics and Statistics College of Science and Mathematics Mindanao State University-Iligan Institute of Technology 9200 Iligan City, Philippines
Email:-*imeldaaniversario@yahoo.com

Keyword:
closed geodetic number of graph, weakly connected closed geodetic set, weakly connected closed geodetic number
Issue Date:
September, 2016
Abstract:

For two vertices u and v of a connected simple graph G, the closed interval IG[u,v] consists of u,v and all vertices lying in some u-v geodesic in G, while for SV(G), the set IG[S] is the union of all sets IG[u,v] for u,v S. In this paper, select vertices of G sequentially as follows: select avertex v1 and let S1 ={v1}. Select a vertex v2  v1 and let
S2={v1,v2}, then determine IG[S2]. If IG[S2]V(G), then successively select a vertex viIG[Si-1] and let Si={v1,v2,...,vi} for i=3,4,...,k. Then determine IG[Si].

A subset S of V (G) is called a weakly connected closed geodetic set of G if the selection of vertex vk in the given manner yields IG[Sk]= V(G), where Sk =S, and Sw is connected, where Sw=N[S], Ewwith Ew consists of edges uvE(G) such that uS or vS. The minimum cardinality of weakly connected closed geodetic set is called the weakly connected closed geodetic number wcgn(G) of G. In this paper, the weakly connected closed geodetic sets of the corona and composition of some graphs are characterized and the weakly connected closed geodetic numbers of these graphs are determined.

Pages:
ISSN:
2319-8044 (Online) - 2231-346X (Print)
Source:
DOI: