On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars
Let G be a finite, simple, and undirected graph with vertex set VG and edge set EG. A super edge-magic labeling of G is a bijection f:VG∪EG⟶1,2,…,VG+EG such that fVG=1,2,…,VG and fu+fuv+fv is a constant for every edge uv∈EG. The super edge-magic labeling f of G is called consecutively super edge-mag...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/4285238 |
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| author | Vira Hari Krisnawati Anak Agung Gede Ngurah Noor Hidayat Abdul Rouf Alghofari |
| author_facet | Vira Hari Krisnawati Anak Agung Gede Ngurah Noor Hidayat Abdul Rouf Alghofari |
| author_sort | Vira Hari Krisnawati |
| collection | DOAJ |
| description | Let G be a finite, simple, and undirected graph with vertex set VG and edge set EG. A super edge-magic labeling of G is a bijection f:VG∪EG⟶1,2,…,VG+EG such that fVG=1,2,…,VG and fu+fuv+fv is a constant for every edge uv∈EG. The super edge-magic labeling f of G is called consecutively super edge-magic if G is a bipartite graph with partite sets A and B such that fA=1,2,…,A and fB=A+1,A+2,…,VG. A graph that admits (consecutively) super edge-magic labeling is called a (consecutively) super edge-magic graph. The super edge-magic deficiency of G, denoted by μsG, is either the minimum nonnegative integer n such that G∪nK1 is super edge-magic or +∞ if there exists no such n. The consecutively super edge-magic deficiency of a graph G is defined by a similar way. In this paper, we investigate the (consecutively) super edge-magic deficiency of subdivision of double stars. We show that, some of them have zero (consecutively) super edge-magic deficiency. |
| format | Article |
| id | doaj-art-e466d65584074e23abee04766e1ddc6c |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e466d65584074e23abee04766e1ddc6c2025-08-20T02:21:34ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/42852384285238On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double StarsVira Hari Krisnawati0Anak Agung Gede Ngurah1Noor Hidayat2Abdul Rouf Alghofari3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Jl. Veteran, Malang, Jawa Timur, IndonesiaDepartment of Civil Engineering, Faculty of Engineering, Universitas Merdeka Malang, Jl. Taman Agung No. 1, Malang, Jawa Timur, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Jl. Veteran, Malang, Jawa Timur, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Jl. Veteran, Malang, Jawa Timur, IndonesiaLet G be a finite, simple, and undirected graph with vertex set VG and edge set EG. A super edge-magic labeling of G is a bijection f:VG∪EG⟶1,2,…,VG+EG such that fVG=1,2,…,VG and fu+fuv+fv is a constant for every edge uv∈EG. The super edge-magic labeling f of G is called consecutively super edge-magic if G is a bipartite graph with partite sets A and B such that fA=1,2,…,A and fB=A+1,A+2,…,VG. A graph that admits (consecutively) super edge-magic labeling is called a (consecutively) super edge-magic graph. The super edge-magic deficiency of G, denoted by μsG, is either the minimum nonnegative integer n such that G∪nK1 is super edge-magic or +∞ if there exists no such n. The consecutively super edge-magic deficiency of a graph G is defined by a similar way. In this paper, we investigate the (consecutively) super edge-magic deficiency of subdivision of double stars. We show that, some of them have zero (consecutively) super edge-magic deficiency.http://dx.doi.org/10.1155/2020/4285238 |
| spellingShingle | Vira Hari Krisnawati Anak Agung Gede Ngurah Noor Hidayat Abdul Rouf Alghofari On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars Journal of Mathematics |
| title | On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars |
| title_full | On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars |
| title_fullStr | On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars |
| title_full_unstemmed | On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars |
| title_short | On the (Consecutively) Super Edge-Magic Deficiency of Subdivision of Double Stars |
| title_sort | on the consecutively super edge magic deficiency of subdivision of double stars |
| url | http://dx.doi.org/10.1155/2020/4285238 |
| work_keys_str_mv | AT viraharikrisnawati ontheconsecutivelysuperedgemagicdeficiencyofsubdivisionofdoublestars AT anakagunggedengurah ontheconsecutivelysuperedgemagicdeficiencyofsubdivisionofdoublestars AT noorhidayat ontheconsecutivelysuperedgemagicdeficiencyofsubdivisionofdoublestars AT abdulroufalghofari ontheconsecutivelysuperedgemagicdeficiencyofsubdivisionofdoublestars |