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arXiv · 1701.08537

Locating-Dominating Sets and Identifying Codes of a Graph Associated to a Finite Vector Space

Muhammad Murtaza·Imran Javaid·Muhammad Fazil
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Abstract

In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das \cite{Das}, such that we can uniquely identify any vertex by examining the vertices that cover it. We use locating-dominating sets and identifying codes, which are closely related concepts for this purpose. These sets consist of a dominating set of graph such that every vertex is uniquely identified by its neighborhood within the dominating sets. We find the location-domination number and the identifying number of the graph and study the exchange property for locating-dominating sets and identifying codes.

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Muhammad Murtaza, Imran Javaid, Muhammad Fazil. 2017-01-30. Locating-Dominating Sets and Identifying Codes of a Graph Associated to a Finite Vector Space. https://arxiv.org/abs/1701.08537

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