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The Resolving Graph of Amalgamation of Cycles

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Relation http://repository.ubaya.ac.id/173/
 
Title The Resolving Graph of Amalgamation of Cycles
 
Creator Iswadi, Hazrul
Baskoro, Edy Tri
Salman, A.N.M
Simanjuntak, Rinovia
 
Subject QA Mathematics
 
Description 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 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 = 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.
 
Publisher The Institute for Combinatorics and its Applications
 
Date 2010
 
Type Article
PeerReviewed
 
Format application/pdf
 
Language en
 
Identifier /173/1/hazrul_The%20Resolving%20Graph%20of%20Amalgamation%20of%20Cycles_2010.pdf
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