On unicyclic graphs of metric dimension 2 with vertices of degree 4

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Date
2018
Authors
Dudenko, Marharyta
Oliynyk, Bogdana
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Abstract
We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension 2 with vertices of degree 4 are characterized.
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Keywords
graph, distance, metric dimension, unicyclic graph, article
Citation
Dudenko M. On unicyclic graphs of metric dimension 2 with vertices of degree 4 / Dudenko M., Oliynyk B. // Algebra and Discrete Mathematics. - 2018. - Vol. 26, Issue 2. - P. 256-269.