06047519

j

06047519 Hungund, N.S. Akka, D.G. Reverse super edge-magic strength of some special trees. Far East J. Appl. Math. 58, No. 1, 1-17 (2011). 2011 Pushpa Publishing House, Allahabad, Uttar Pradesh, India EN reverse super edge-magic labeling reverse super edge-magic strength of a graph the path

http://www.pphmj.com/abstract/6230.htm

Summary: In this paper, we introduce a new concept of reverse super edge-magic labeling and reverse super edge-magic strength of a graph $G$. A graph $G$ is said to be reverse super edge-magic if there exists a bijection $f:V\cup E\to\{1,2,\ldots ,p+q\}$ such that $f(uv)-[f(u)+f(v)]$ is a constant, for all $uv\in E$ and $f(V)=\{1,2,\ldots ,p\}$ Such a bijection is called a reverse super edge-magic labeling and the minimum of all constants is called a reverse super edge-magic strength of the graph $G$, where the minimum is taken over all reverse super edge-magic labelings of $G$. Also, we obtain the reverse super edge-magic labelings and reverse super edge-magic strength of some well known graphs such as the path $P_{n}$ the tree $\langle K_{1,m}:P_{n} \rangle$ the bistar $B_{m,n}$ the tree $\langle K_{1,m}:K_{1,n} \rangle$ and the banana tree $BT(n_{1},n_{2},\ldots ,n_{k})$.