On Super Mean Labeling for Total Graph of Path and Cycle
Let G(V,E) be a graph with the vertex set V and the edge set E, respectively. By a graph G=(V,E) we mean a finite undirected graph with neither loops nor multiple edges. The number of vertices of G is called order of G and it is denoted by p. Let G be a (p,q) graph. A super mean graph on G is an inj...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/9250424 |
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| author | Nur Inayah I. Wayan Sudarsana Selvy Musdalifah Nurhasanah Daeng Mangesa |
| author_facet | Nur Inayah I. Wayan Sudarsana Selvy Musdalifah Nurhasanah Daeng Mangesa |
| author_sort | Nur Inayah |
| collection | DOAJ |
| description | Let G(V,E) be a graph with the vertex set V and the edge set E, respectively. By a graph G=(V,E) we mean a finite undirected graph with neither loops nor multiple edges. The number of vertices of G is called order of G and it is denoted by p. Let G be a (p,q) graph. A super mean graph on G is an injection f:V→{1,2,3…,p+q} such that, for each edge e=uv in E labeled by f⁎e=fu+f(v)/2, the set fV∪{f⁎e:e∈E} forms 1,2,3,…,p+q. A graph which admits super mean labeling is called super mean graph. The total graph T(G) of G is the graph with the vertex set V∪E and two vertices are adjacent whenever they are either adjacent or incident in G. We have showed that graphs T(Pn) and TCn are super mean, where Pn is a path on n vertices and Cn is a cycle on n vertices. |
| format | Article |
| id | doaj-art-b215cd372be4403c9fe4a96e15b153a4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
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| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b215cd372be4403c9fe4a96e15b153a42025-02-03T07:25:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/92504249250424On Super Mean Labeling for Total Graph of Path and CycleNur Inayah0I. Wayan Sudarsana1Selvy Musdalifah2Nurhasanah Daeng Mangesa3Mathematics Department, Faculty of Sciences and Technology, State Islamic University of Syarif Hidayatullah, Jakarta, IndonesiaCombinatorial and Applied Mathematics Research Group (CAMRG), Department of Mathematics, Faculty of Mathematics and Natural Sciences, Tadulako University, Palu, IndonesiaCombinatorial and Applied Mathematics Research Group (CAMRG), Department of Mathematics, Faculty of Mathematics and Natural Sciences, Tadulako University, Palu, IndonesiaCombinatorial and Applied Mathematics Research Group (CAMRG), Department of Mathematics, Faculty of Mathematics and Natural Sciences, Tadulako University, Palu, IndonesiaLet G(V,E) be a graph with the vertex set V and the edge set E, respectively. By a graph G=(V,E) we mean a finite undirected graph with neither loops nor multiple edges. The number of vertices of G is called order of G and it is denoted by p. Let G be a (p,q) graph. A super mean graph on G is an injection f:V→{1,2,3…,p+q} such that, for each edge e=uv in E labeled by f⁎e=fu+f(v)/2, the set fV∪{f⁎e:e∈E} forms 1,2,3,…,p+q. A graph which admits super mean labeling is called super mean graph. The total graph T(G) of G is the graph with the vertex set V∪E and two vertices are adjacent whenever they are either adjacent or incident in G. We have showed that graphs T(Pn) and TCn are super mean, where Pn is a path on n vertices and Cn is a cycle on n vertices.http://dx.doi.org/10.1155/2018/9250424 |
| spellingShingle | Nur Inayah I. Wayan Sudarsana Selvy Musdalifah Nurhasanah Daeng Mangesa On Super Mean Labeling for Total Graph of Path and Cycle International Journal of Mathematics and Mathematical Sciences |
| title | On Super Mean Labeling for Total Graph of Path and Cycle |
| title_full | On Super Mean Labeling for Total Graph of Path and Cycle |
| title_fullStr | On Super Mean Labeling for Total Graph of Path and Cycle |
| title_full_unstemmed | On Super Mean Labeling for Total Graph of Path and Cycle |
| title_short | On Super Mean Labeling for Total Graph of Path and Cycle |
| title_sort | on super mean labeling for total graph of path and cycle |
| url | http://dx.doi.org/10.1155/2018/9250424 |
| work_keys_str_mv | AT nurinayah onsupermeanlabelingfortotalgraphofpathandcycle AT iwayansudarsana onsupermeanlabelingfortotalgraphofpathandcycle AT selvymusdalifah onsupermeanlabelingfortotalgraphofpathandcycle AT nurhasanahdaengmangesa onsupermeanlabelingfortotalgraphofpathandcycle |