Iswadi, Hazrul and Baskoro, Edy Tri and Salman, A.N.M and Simanjuntak, Rinovia (2010) The Resolving Graph of Amalgamation of Cycles. Utilitas Mathematica, 83. pp. 121-132. ISSN 0315-3681
Preview |
PDF
hazrul_The Resolving Graph of Amalgamation of Cycles_2010.pdf Download (173kB) | Preview |
Abstract
For an ordered set W = {w_1,w_2,...,w_k} of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple r(v|W) = (d(v,w_1),d(v,w_2),...,d(v,w_k)) where d(x,y) represents the distance between the vertices x and y. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for G. The dimension of G, denoted by dim(G), is the number of vertices in a basis of G. A resolving set W of G is connected if the subgraph <W> induced by W is a nontrivial connected subgraph of G. The connected resolving number is the minimum cardinality of a connected resolving set in a graph G, denoted by cr(G). A cr-set of G is a connected resolving set with cardinality cr(G). A connected graph H is a resolving graph if there is a graph G with a cr-set W such that <W> = H. Let {G_i} be a finite collection of graphs and each G_i has a fixed vertex v_{oi} called a terminal. The amalgamation Amal{Gi,v_{oi}} is formed by taking of all the G_i's and identifying their terminals. In this paper, we determine the connected resolving number and characterize the resolving graphs of amalgamation of cycles.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Resolving Graph, Resolving Set, Amalgamation, Cyacles |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Academic Department > Department of Mathematics and Natural Science |
| Depositing User: | Hazrul Iswadi 6179 |
| Date Deposited: | 08 Mar 2012 07:04 |
| Last Modified: | 20 Mar 2012 01:41 |
| URI: | http://repository.ubaya.ac.id/id/eprint/173 |
Actions (login required)
 |
View Item |
