On Super (a,d)-Edge-Antimagic Total Labeling of Special Types of Crown Graphs
For a graph G=(V,E), a bijection f from V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} is called (a,d)-edge-antimagic total ((a,d)-EAT) labeling of G if the edge-weights w(xy)=f(x)+f(y)+f(xy),xy∈E(G), form an arithmetic progression starting from a and having a common difference d, where a>0 and d≥0 are two fixe...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/896815 |
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| Summary: | For a graph G=(V,E), a bijection f from V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} is called (a,d)-edge-antimagic total ((a,d)-EAT) labeling of G if the edge-weights w(xy)=f(x)+f(y)+f(xy),xy∈E(G), form an arithmetic progression starting from a and having a common difference d, where a>0 and d≥0 are two fixed integers. An (a,d)-EAT labeling is called super (a,d)-EAT labeling if the vertices are labeled with the smallest possible numbers; that is, f(V)={1,2,…,|V(G)|}. In this paper, we study super (a,d)-EAT labeling of cycles with some pendant edges attached to different vertices of the cycle. |
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| ISSN: | 1110-757X 1687-0042 |