Open AccessThe mixed metric dimension of wheel-like graphs
Author(s) -
Darmaji,
Nadia Azahra
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2157/1/012010
Subject(s) - combinatorics , mathematics , metric dimension , distance regular graph , graph power , wheel graph , bound graph , discrete mathematics , vertex (graph theory) , neighbourhood (mathematics) , graph , strongly regular graph , complement graph , line graph , 1 planar graph , mathematical analysis
Consider the graph G = ( V, E ). It is a connected graph. It is a simple graph too. A node w ∈ V , then we call vertex, determined two elements of graph. There are vertices and edges of graphs. Any two vertices x, y ∈ E ∪ V if d ( w, x ) ≠ d ( w, y ), which d ( w, x ) and d ( w, y ) is the mixed distance of the element w (vertices or edges) in graph G . A set of vertices in a graph G is represented by the symbol R m that defines a mixed metric generator for G , if the elements of vertices or edges are stipulated by several vertex set of R m . There’s a chance that some mixed metric generators have varied cardinality. We choose one whose the minimum cardinality and it is called the mixed metric dimension of graph G , denoted by dim m ( G ). This research examines the mixed metric dimension of gear G n , helm H n , sunflower SF n , and friendship graph Fr n . We call these graphs by wheel-like graphs. Our findings include the mixed metric dimension of gear graph G n of order n ≥ 4 is dim m ( G n ) = n , helm graph H n of order n ≥ 4 is dim m ( H n ) = n , sunflower graph SF n of order n ≥ 5 is dim m ( SF n ) = n and friendship graph Fr n of order n ≥ 3 is dim m ( Fr n ) = 2 n .