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

• Published in: Algebra and Discrete Mathematics
• Date: 2018
• Main Authors: Dudenko, M., Oliynyk, B.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188412
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On unicyclic graphs of metric dimension 2 with vertices of degree 4 / M. Dudenko, B. Oliynyk // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 256–269. — Бібліогр.: 13 назв. — англ.

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 constr...