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All Journal Limits: Journal of Mathematics and Its Applications
Muhammad Ridwan
Universitas Islam Negeri Alauddin Makassar
Computer Science & IT Mathematics

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Bilangan Pembeda Tanpa Titik Terisolasi Graf W_n⊙K_1dan F_n⊙K_1 Wahyuni Abidin; Ismail Mulia Hasibuan; Try Azisah Nurman; Muhammad Ridwan
Limits: Journal of Mathematics and Its Applications Vol. 23 No. 1 (2026): Limits: Journal of Mathematics and Its Applications Volume 23 Nomor 1 Edisi Ap
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v23i1.7683

Abstract

Let  be a graph and  be an ordered subset of the vertex set og graph  The representation of a vertex  in  with respect to is defined as , where  is the distance between vertex  and  for all $ The set  is called a resolving set of  if the representation of every vertex in  is distinct. A resolving set with the minimum cardinality is called a basis of  and the cardinality of a basis of  is the metric dimension of the graph . A vertex in  is called an isolated vertex if there are no edges incident to . A resolving set  is called a non-isolated resolving set if the subgraph induced by does not contain isolated vertices. A non-isolated resolving set with the minimum cardinality is called an -basis of , and the number of its members is called the non-isolated resolving number of , nonated by . In this paper, we discuss non-isolated resolving numbers of a graph obtained from the corona product of two graphs. The corona product of graph  and graph , denoted by , is a graph obtained by taking one copy of  and as many copies of  as there are vertices in , then connecting every vertex from the -th copy of  to the -th vertex in . The results show that if  is a wheel graph or a fan graph, then the non-isolated resolving number of the corona product  depends on the number of vertices in the graph
Co-Authors Ismail Mulia Hasibuan Wahyuni Abidin