Super (a, d)-H-antimagic labeling of subdivided graphs
A simple graph G = (V, E) admits an H-covering, if every edge in E(G) belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called an (a, d)-H-antimagic if there exists a bijective function f : V(G) ∪ E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphs H′ isomorp...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-06-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2018-0062 |
| _version_ | 1818574858106175488 |
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| author | Taimur Amir Numan Muhammad Ali Gohar Mumtaz Adeela Semaničová-Feňovčíková Andrea |
| author_facet | Taimur Amir Numan Muhammad Ali Gohar Mumtaz Adeela Semaničová-Feňovčíková Andrea |
| author_sort | Taimur Amir |
| collection | DOAJ |
| description | A simple graph G = (V, E) admits an H-covering, if every edge in E(G) belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called an (a, d)-H-antimagic if there exists a bijective function f : V(G) ∪ E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphs H′ isomorphic to H the sums ∑v∈V(H′)f(v) + ∑e∈E(H′)f(e) form an arithmetic sequence {a, a + d, …, a + (t − 1)d}, where a > 0 and d ≥ 0 are integers and t is the number of all subgraphs of G isomorphic to H. Moreover, if the vertices are labeled with numbers 1, 2, …, |V(G)| the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an (a, d)-cycle-antimagic labeling for some d. |
| first_indexed | 2024-12-15T00:31:37Z |
| format | Article |
| id | doaj.art-dae76ad4890b4a3c9231663520edf7f8 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-15T00:31:37Z |
| publishDate | 2018-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-dae76ad4890b4a3c9231663520edf7f82022-12-21T22:42:00ZengDe GruyterOpen Mathematics2391-54552018-06-0116168869710.1515/math-2018-0062math-2018-0062Super (a, d)-H-antimagic labeling of subdivided graphsTaimur Amir0Numan Muhammad1Ali Gohar2Mumtaz Adeela3Semaničová-Feňovčíková Andrea4Department of Mathematics, Islamia College Peshawar, Peshawar, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, Attock, PakistanDepartment of Mathematics, Islamia College Peshawar, Peshawar, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, Attock, PakistanDepartment of Applied Mathematics and Informatics, Technical University, Košice, Slovak RepublicA simple graph G = (V, E) admits an H-covering, if every edge in E(G) belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called an (a, d)-H-antimagic if there exists a bijective function f : V(G) ∪ E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphs H′ isomorphic to H the sums ∑v∈V(H′)f(v) + ∑e∈E(H′)f(e) form an arithmetic sequence {a, a + d, …, a + (t − 1)d}, where a > 0 and d ≥ 0 are integers and t is the number of all subgraphs of G isomorphic to H. Moreover, if the vertices are labeled with numbers 1, 2, …, |V(G)| the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an (a, d)-cycle-antimagic labeling for some d.https://doi.org/10.1515/math-2018-0062h-covering(super) (a, d)-h-antimagic labelingsubdivided graphsubdivided wheel05c78 |
| spellingShingle | Taimur Amir Numan Muhammad Ali Gohar Mumtaz Adeela Semaničová-Feňovčíková Andrea Super (a, d)-H-antimagic labeling of subdivided graphs Open Mathematics h-covering (super) (a, d)-h-antimagic labeling subdivided graph subdivided wheel 05c78 |
| title | Super (a, d)-H-antimagic labeling of subdivided graphs |
| title_full | Super (a, d)-H-antimagic labeling of subdivided graphs |
| title_fullStr | Super (a, d)-H-antimagic labeling of subdivided graphs |
| title_full_unstemmed | Super (a, d)-H-antimagic labeling of subdivided graphs |
| title_short | Super (a, d)-H-antimagic labeling of subdivided graphs |
| title_sort | super a d h antimagic labeling of subdivided graphs |
| topic | h-covering (super) (a, d)-h-antimagic labeling subdivided graph subdivided wheel 05c78 |
| url | https://doi.org/10.1515/math-2018-0062 |
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