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Graphs Whose Mixed Metric Dimension Is Equal to Their Order by Ali Ghalavand; Sandi Klavžar; Mostafa Tavakoli is a Mathematics article available to read on EtoBox.

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The mixed metric dimension mdim(G) of a graph G is the cardinality of a smallest set of vertices that (metrically) resolves each pair of elements from V (G)∪ E(G). We say that G is a max-mdim graph if mdim(G) = n(G). It is proved that a max-mdim graph G with n(G) ≥ 7 contains a vertex of degree at least 5. Using the strong product of graphs and amalgamations, large families of max-mdim graphs are constructed. The mixed metric dimension of graphs with at least one universal vertex is determined. The mixed metric dimension of graphs G with cut vertices is bounded from the above and the mixed metric dimension of block graphs computed. Keywords Resolving set • Mixed resolving set • Strong product of graphs • Cut vertex • Chemical graphs • Block graphs Mathematics Subject Classification 05C12 B Mostafa Tavakoli

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Author

Ali Ghalavand; Sandi Klavžar; Mostafa Tavakoli

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)