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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 13 > No. S1

 
   

On Face Magic Labeling of Duplication of a Tree

PP: 275-278
doi:10.18576/amis/13S130
Author(s)
B. Roopa, L. Shobana, R. Kalaiyarasi,
Abstract
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. Let $(a, b, c) \in \{0, 1\}$. A labeling of type $(a, b, c)$ assigns labels from the set $\{1, 2, \dots, a|V(G)|+b|E(G)|+c|F(G)|\}$ to the vertices, edges and faces of $G$ in such a way that each vertex receives $a$ labels, each edge receives $b$ labels and each face receives $c$ labels and each number is used exactly once without repetition as a label. The weight of the face $w(f)$ under a labeling is the sum of the labels of the face itself together with the labels of vertices and edges surrounding that face. A labeling of type $(a, b, c)$ is said to be face magic, if for every positive integer $k$ all $k$-sided faces have the same weight. Here we study the existence of face magic labeling of duplication and double duplication of trees.

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