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On Face Magic Labeling of Duplication of a Tree |
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PP: 275-278 |
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doi:10.18576/amis/13S130
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Author(s) |
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B. Roopa,
L. Shobana,
R. Kalaiyarasi,
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Abstract |
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| 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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