Perfect (super) Edge-Magic Crowns
A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2, ,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence. An ed...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/66441 |
| Acesso em linha: | https://doi.org/10.1007/s00025-016-0643-7 http://hdl.handle.net/10459.1/66441 |
| Access Level: | acceso abierto |
| Palavra-chave: | Edge-magic Super edge-magic Valence Perfect (super) edge-magic |
| Resumo: | A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2, ,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence. An edge-magic labelling with the extra property that f(V(G))={1,2, ,|V(G)|} is called super edge-magic. A graph is called perfect (super) edge-magic if all theoretical (super) edge-magic valences are possible. In this paper we continue the study of the valences for (super) edge-magic labelings of crowns Cm⊙K¯¯¯¯¯n and we prove that the crowns are perfect (super) edge-magic when m=pq where p and q are different odd primes. We also provide a lower bound for the number of different valences of Cm⊙K¯¯¯¯¯n , in terms of the prime factors of m. |
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