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- W4283642692 abstract "Let G be a finite, simple, and connected graph with the vertex set V and the edge set E. The distance between the vertex u and the edge e=vw is defined as d(u,e)=min{d(u,v),d(u,w)}. A vertex x distinguishes two edges e1,e2 if d(x,e1)≠d(x,e2). A subset Le of V is called an edge metric generator for G if every two distinct edges of G are distinguished by some vertex of Le. The minimum cardinality of an edge metric generator for G is called the edge metric dimension and is denoted by dime(G). Similarly, a vertex x distinguishes two elements (vertices or edges) u,v∈V∪E if d(x,u)≠d(x,v). A subset Lm of V is called a mixed metric generator for G if every two distinct elements (vertices and edges) of G are distinguished by some vertex of Lm. The minimum cardinality of a mixed metric generator for G is called the mixed metric dimension and is denoted by dimm(G). In this paper, we study the edge metric dimension and mixed metric dimension of planar graph Qn. We prove that the edge metric dimension and the mixed metric dimension of Qn are both finite and do not depend upon the number of vertices." @default.
- W4283642692 created "2022-06-29" @default.
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- W4283642692 date "2022-10-01" @default.
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- W4283642692 title "Edge metric dimension and mixed metric dimension of planar graph <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e39 altimg=si150.svg><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>" @default.
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- W4283642692 doi "https://doi.org/10.1016/j.dam.2022.06.023" @default.
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