2024
DOI: 10.3934/math.2024795
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On the edge metric dimension of some classes of cacti

Lyimo Sygbert Mhagama,
Muhammad Faisal Nadeem,
Mohamad Nazri Husin

Abstract: <abstract><p>The cactus graph has many practical applications, particularly in radio communication systems. Let $ G = (V, E) $ be a finite, undirected, and simple connected graph, then the edge metric dimension of $ G $ is the minimum cardinality of the edge metric generator for $ G $ (an ordered set of vertices that uniquely determines each pair of distinct edges in terms of distance vectors). Given an ordered set of vertices $ \mathcal{G}_e = \{g_1, g_2, ..., g_k \} $ of a connected graph $ G $, … Show more

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