Iswadi, Hazrul (2016) BIRESOLVING GRAPH OF CYCLERELATED GRAPHS. In: The Asian Mathematical Conference 2016 (AMC 2016), July 2529,2016, Bali. (Unpublished)

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Abstract
Let $G(V,E)$ be a simple connected graph. For each $x \in V$, we associate a pair of vectors $S_x = (u,v)$ with respect to $S = \{s_1, s_2, \cdots, s_k\} \subseteq V$, where $u = (d(x,s_1), d(x,s_2), \cdots, d(x,s_k))$ and $v = (\delta(x,s_1), \delta(x,s_2), \cdots, \delta(x,s_k))$, where $d(x,s_i)$ and $\delta(x,s_i)$ respectively denote the lengths of a shortest and longest path between $x$ and $s_i$. The set $S$ is said to biresolving set $G$ if every vertex of $G$ has a distinct pair of vectors. The minimum cardinality of a biresolving set is called bimetric dimension of $G$. A biresolving set $S$ is connected if the subgraph $\langle S \rangle$ induced by $S$ is a nontrivial connected subgraph of $G$. The connected biresolving number is the minimum cardinality of a connected biresolving set in a graph $G$, denoted by $cbr(G)$. A \textit{cbr}set of $G$ is a connected biresolving set with cardinality $cbr(G)$. A connected graph $H$ is a \textit{biresolving graph} if there is a graph $G$ with a cbrset $W$ such that $\langle W \rangle = H$. In this paper we show bimetric dimension and biresolving graph of cyclerelated graphs.
Item Type:  Conference or Workshop Item (Poster) 

Uncontrolled Keywords:  biresolving set, bimetric dimension, connected bireso lving number, connected biresolving set, biresolving graph 
Subjects:  Q Science > QA Mathematics 
Divisions:  Academic Department > Department of Mathematics and Natural Science 
Depositing User:  Hazrul Iswadi 6179 
Date Deposited:  04 Jul 2018 04:02 
Last Modified:  04 Jul 2018 04:02 
URI:  http://repository.ubaya.ac.id/id/eprint/32609 
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