On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs
An (a,d)-H-antimagic total labeling of a simple graph G admitting an H-covering is a bijection φ:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that for all subgraphs H′ of G isomorphic to H, the set of H′-weights given by wtφ(H′)=∑v∈V(H′)φ(v)+∑e∈E(H′)φ(e) forms an arithmetic sequence a,a+d,…,a+(t−1)d where a...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-10-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844021023069 |
| _version_ | 1818896898201747456 |
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| author | Nur Inayah Faisal Susanto Andrea Semaničová-Feňovčíková |
| author_facet | Nur Inayah Faisal Susanto Andrea Semaničová-Feňovčíková |
| author_sort | Nur Inayah |
| collection | DOAJ |
| description | An (a,d)-H-antimagic total labeling of a simple graph G admitting an H-covering is a bijection φ:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that for all subgraphs H′ of G isomorphic to H, the set of H′-weights given by wtφ(H′)=∑v∈V(H′)φ(v)+∑e∈E(H′)φ(e) forms an arithmetic sequence a,a+d,…,a+(t−1)d where a>0, d⩾0 are two fixed integers and t is the number of all subgraphs of G isomorphic to H. Moreover, such a labeling φ is called super if the smallest possible labels appear on the vertices. A (super) (a,d)-H-antimagic graph is a graph that admits a (super) (a,d)-H-antimagic total labeling. In this paper the existence of super (a,d)-H-antimagic total labelings for the m-shadow and the closed m-shadow of a connected G for several values of d is proved. |
| first_indexed | 2024-12-19T19:07:35Z |
| format | Article |
| id | doaj.art-8dc085de30274d9b828cc2b62571a6b2 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-12-19T19:07:35Z |
| publishDate | 2021-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-8dc085de30274d9b828cc2b62571a6b22022-12-21T20:09:24ZengElsevierHeliyon2405-84402021-10-01710e08203On H-antimagic coverings for m-shadow and closed m-shadow of connected graphsNur Inayah0Faisal Susanto1Andrea Semaničová-Feňovčíková2Department of Mathematics, Faculty of Science and Technology, Syarif Hidayatullah State Islamic University Jakarta, Jalan Ir. H. Djuanda 95, Ciputat 15412, Indonesia; Corresponding author.Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Tadulako, Jalan Soekarno Hatta Km. 9, Palu 94118, IndonesiaDepartment of Applied Mathematics and Informatics, Technical University, Letná 9, Košice, SlovakiaAn (a,d)-H-antimagic total labeling of a simple graph G admitting an H-covering is a bijection φ:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that for all subgraphs H′ of G isomorphic to H, the set of H′-weights given by wtφ(H′)=∑v∈V(H′)φ(v)+∑e∈E(H′)φ(e) forms an arithmetic sequence a,a+d,…,a+(t−1)d where a>0, d⩾0 are two fixed integers and t is the number of all subgraphs of G isomorphic to H. Moreover, such a labeling φ is called super if the smallest possible labels appear on the vertices. A (super) (a,d)-H-antimagic graph is a graph that admits a (super) (a,d)-H-antimagic total labeling. In this paper the existence of super (a,d)-H-antimagic total labelings for the m-shadow and the closed m-shadow of a connected G for several values of d is proved.http://www.sciencedirect.com/science/article/pii/S2405844021023069Super (a,d)-antimagic total labelingSuper (a,d)-H-antimagic graphH-coveringm-shadow of a graphClosed m-shadow of a graph |
| spellingShingle | Nur Inayah Faisal Susanto Andrea Semaničová-Feňovčíková On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs Heliyon Super (a,d)-antimagic total labeling Super (a,d)-H-antimagic graph H-covering m-shadow of a graph Closed m-shadow of a graph |
| title | On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs |
| title_full | On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs |
| title_fullStr | On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs |
| title_full_unstemmed | On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs |
| title_short | On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs |
| title_sort | on h antimagic coverings for m shadow and closed m shadow of connected graphs |
| topic | Super (a,d)-antimagic total labeling Super (a,d)-H-antimagic graph H-covering m-shadow of a graph Closed m-shadow of a graph |
| url | http://www.sciencedirect.com/science/article/pii/S2405844021023069 |
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