SARI, VIANITA and Sumanto, Y.D. and IRAWANTO, BAMBANG (2010) *GRAF GENAP.* Undergraduate thesis, Fakultas Matematika dan Ilmu Pengetahuan Alam.

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## Abstract

A graph G is called even if for each vertex v∈G there is a unique buddy v ̅∈G, and d(v,v ̅ ) = diam G. In this final assigment will be explained about the properties of even graph and special even graph. For an even graph of order n and diameter d other than an even cycle graph it is shown that n≥3d-1. Some kind of special even graphs are even graph balanced, even graph harmonic, and even graph symmetric. An even graph G is called balanced if deg〖v=degv ̅ 〗 for each v ∈V(G), harmonic if uv ∈E(G) than u ̅ v ̅ ∈E(G) for all u,v ∈V(G), and symmetric if d(u,v)+d(u,v ̅ )=diam G for all u,v ∈V(G). For an even graph symmetric of order n and diameter d other than an even cycle graph it is shown that n≥3d-1. Union and join from two even graphs are not always even. In the other hand, Cartesian product of two even graphs are always even.

Item Type: | Thesis (Undergraduate) |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science and Mathematics > Department of Mathematics |

ID Code: | 26891 |

Deposited By: | Ms Niken P |

Deposited On: | 20 Apr 2011 08:53 |

Last Modified: | 20 Apr 2011 08:53 |

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