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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| Format: | Article |
| Language: | English |
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2023-05-01
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| 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. |
| format | Article |
| id | doaj-art-014f98021cb042efbcb7d98f59e45a5e |
| institution | DOAJ |
| issn | 2086-0382 2477-3344 |
| 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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