Local multiset dimension of corona product on tree graphs

Ridho Alfarisi, Liliek Susilowati, Dafik, Arika Indah Kristiana

Research output: Contribution to journalArticlepeer-review

Abstract

One of the topics of distance in graphs is resolving set problem. This topic has many applications in science and technology namely navigation robots, chemistry structure, and computer sciences. Suppose the set W = {s1,s2,...,sk}⊂ V (G), the vertex representations of x V (G) is rm(x|W) = {d(x,s1),d(x,s2),...,d(x,sk)}, where d(x,si) is the length of the shortest path of the vertex x and the vertex in W together with their multiplicity. The set W is called a local m-resolving set of graphs G if rm(v|W)≠rm(u|W) for uv E(G). The local m-resolving set having minimum cardinality is called the local multiset basis and its cardinality is called the local multiset dimension of G, denoted by mdl(G). In our paper, we determine the establish bounds of local multiset dimension of graph resulting corona product of tree graphs.

Original languageEnglish
Article number2350092
JournalDiscrete Mathematics, Algorithms and Applications
DOIs
Publication statusAccepted/In press - 2023

Keywords

  • Local m -resolving set
  • corona product
  • local multiset dimension
  • tree graphs

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