Bashir, Fozia (2010) *Face Labelings of Graphs.* PhD thesis, Govt. College University, Lahore.

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## Abstract

The thesis deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a di erence d. Such a labeling is called super if the smallest possible labels appear on the vertices. The thesis is devoted to study of super d-antimagic labelings of type (1; 1; 1) for antiprisms and disjoint union of prisms. We consider the antiprism and prism as three cycle parts: the outer cycle, the inner cycle and the middle cycle. To label the inner, the outer and the middle cycles we use the edge-antimagic total labelings and the vertex-antimagic total labelings. These labelings combine to a resulting super d-antimagic labeling of type (1; 1; 1) for the required values of di erence d

Item Type: | Thesis (PhD) |
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Uncontrolled Keywords: | Face, Labelings, Graphs, Sampling, literature, household |

Subjects: | Physical Sciences (f) > Mathematics(f5) |

ID Code: | 5973 |

Deposited By: | Mr. Javed Memon |

Deposited On: | 01 Feb 2011 09:07 |

Last Modified: | 01 Feb 2011 09:07 |

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