The Distance Irregular Reflexive k-Labeling of Graphs

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...

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Main Authors: Ika Hesti Agustin, Dafik Dafik, N. Mohanapriya, Marsidi Marsidi, Ismail Naci Cangul
Format: Article
Language:English
Published: Mathematics Department UIN Maulana Malik Ibrahim Malang 2023-05-01
Series:Cauchy: Jurnal Matematika Murni dan Aplikasi
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Online Access:https://ejournal.uin-malang.ac.id/index.php/Math/article/view/19747
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author Ika Hesti Agustin
Dafik Dafik
N. Mohanapriya
Marsidi Marsidi
Ismail Naci Cangul
author_facet Ika Hesti Agustin
Dafik Dafik
N. Mohanapriya
Marsidi Marsidi
Ismail Naci Cangul
author_sort Ika Hesti Agustin
collection DOAJ
description 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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issn 2086-0382
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language English
publishDate 2023-05-01
publisher Mathematics Department UIN Maulana Malik Ibrahim Malang
record_format Article
series Cauchy: Jurnal Matematika Murni dan Aplikasi
spelling doaj-art-014f98021cb042efbcb7d98f59e45a5e2025-08-20T03:11:51ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442023-05-017462262910.18860/ca.v7i4.197477020The Distance Irregular Reflexive k-Labeling of GraphsIka Hesti Agustin0Dafik Dafik1N. Mohanapriya2Marsidi Marsidi3Ismail Naci Cangul4Department of Mathematics, University of Jember, Indonesia.Department of Mathematics Education, University of Jember, IndonesiaDepartment of Mathematics, Kongunadu Arts and Science College, IndiaDepartment of Mathematics Education, University of PGRI Argopuro Jember, IndonesiaUludag University, Mathematics Department, Gorukle 16059 Bursa, TurkeyA 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.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/19747distance irregular reflexive k-labelingdistance reflexive strengthpathstarfriendship
spellingShingle Ika Hesti Agustin
Dafik Dafik
N. Mohanapriya
Marsidi Marsidi
Ismail Naci Cangul
The Distance Irregular Reflexive k-Labeling of Graphs
Cauchy: Jurnal Matematika Murni dan Aplikasi
distance irregular reflexive k-labeling
distance reflexive strength
path
star
friendship
title The Distance Irregular Reflexive k-Labeling of Graphs
title_full The Distance Irregular Reflexive k-Labeling of Graphs
title_fullStr The Distance Irregular Reflexive k-Labeling of Graphs
title_full_unstemmed The Distance Irregular Reflexive k-Labeling of Graphs
title_short The Distance Irregular Reflexive k-Labeling of Graphs
title_sort distance irregular reflexive k labeling of graphs
topic distance irregular reflexive k-labeling
distance reflexive strength
path
star
friendship
url https://ejournal.uin-malang.ac.id/index.php/Math/article/view/19747
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