CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

The Distance Irregular Reflexive k-Labeling of Graphs

Ika Hesti Agustin (Department of Mathematics, University of Jember, Indonesia.)
Dafik Dafik (Department of Mathematics Education, University of Jember, Indonesia)
N. Mohanapriya (Department of Mathematics, Kongunadu Arts and Science College, India)
Marsidi Marsidi (Department of Mathematics Education, University of PGRI Argopuro Jember, Indonesia)
Ismail Naci Cangul (Uludag University, Mathematics Department, Gorukle 16059 Bursa, Turkey)



Article Info

Publish Date
24 May 2023

Abstract

A total k-labeling is a function fe from the edge set to the set {1, 2, . . . , ke} and a function fv from the vertex set to the set {0, 2, 4, . . . , 2kv}, where k = max{ke, 2kv}. A distance irregular reflexive k-labeling of the graph G is the total k-labeling, if for every two different vertices u and u 0 of G, w(u) 6= w(u 0 ), where w(u) = Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum k for graph G which has a distance irregular reflexive k-labelling is called distance reflexive strength of the graph G, denoted by Dref (G). In this paper, we determine the exact value of distance reflexive strength of some connected graphs, namely path, star, and friendship graph.

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Journal Info

Abbrev

Math

Publisher

Subject

Mathematics

Description

Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh ...