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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Sullystiawati, Lusia Herni
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Mathematics

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On H-irregular reflexive labeling of graph Marsidi, Marsidi; Agustin, Ika Hesti; Dafik, Dafik; Rahman, Md. Saidur; Sullystiawati, Lusia Herni
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.23753

Abstract

By an irregular reflexive  labeling, we mean a function  and  such that  if  and  if , where  max . Let , the irregular reflexive  labeling is called an -irregular reflexive -labeling of graph  if every two different sub graphs  and  isomorphic to , it holds , where . The minimum  for graph  which has an -irregular reflexive -labeling is called the reflexive  strength of graph and denoted by . In this paper we initiate to study the lower bound of the reflexive  strenght of graphs and the reflexive  strenght of flower, Shack  and book graph, where  isomorphic to and , respectively.
The Reflexive H-Strength on Some Graphs Sullystiawati, Lusia Herni; Marsidi, Marsidi; Putra, Eric Dwi; Agustin, Ika Hesti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i1.23172

Abstract

Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G).  The irregular reflexive -labeling is defined by the function  and  such that  if  and  if , where  max . The irregular reflexive  labeling is called an -irregular reflexive -labeling of the graph  if every two different sub graphs  and  isomorphic to  it holds , where  for the sub graph . The minimum  for graph  which has an -irregular reflexive -labelling is called the reflexive  strength of the graph  and denoted by . In this paper we determine the lower bound of the reflexive  strength of some subgraphs,  on , the sub graph  on  the sub graph  on  and the sub graph  on .
Co-Authors D. Dafik Ika Hesti Agustin, Ika Hesti Putra, Eric Dwi Rahman, Md. Saidur