On mixed metric dimension in subdivision, middle, and total graphs
نویسندگان
چکیده
Let G be a graph and let S(G), M(G), T(G) the subdivision, middle, total of G, respectively. dim(G), edim(G), mdim(G) metric dimension, edge mixed dimension In this paper, for subdivision it is proved that max{dim(G), edim(G)} ≤ mdim(S(G)) mdim(G). A family graphs Gn constructed which mdim(Gn) − mdim(S(Gn)) ≥ 2 holds shows inequality can strict, while cactus = For middle dim(M(G)) holds, if tree with n1(G) leaves, then n1(G). Moreover, mdim(T (G)) 2n1(G) dim(G) dim(T hold when tree.
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ژورنال
عنوان ژورنال: Quaestiones Mathematicae
سال: 2023
ISSN: ['1727-933X', '1607-3606']
DOI: https://doi.org/10.2989/16073606.2023.2169206