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The Weak q-DCI Properties of Metacyclic Group of Order qp

Author: ChenYuanFang
Tutor: XuShangJin
School: Guangxi University
Course: Basic mathematics
Keywords: Metacyclic group Cayley graph Isomorphic DCI- sex
CLC: O152
Type: Master's thesis
Year: 2005
Downloads: 32
Quote: 0
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Abstract


The graph symmetry has always been a hot issue in the study group with Figure . It is mainly through the graph automorphism group has some symmetry to describe . A typical representative of such plans is the Cayley graph Sabidussi coset graph . The Cayley graph automorphism problem is divided into two aspects: one is to explore a group when the Cayley graph isomorphism ; the other hand , different groups may Cayley graph isomorphism . In recent years , people are more concentrated to the previous question , and mostly limited to the nature of the so-called CI . 1967 Adam conjecture opened a prelude to the CI- group and DCI- group research . Exchange group and solvable , CI - - of the research has been quite thorough . For DCI- metacyclic group known results . In 1979 , Babai and Frankl proposed the conjecture : For any odd prime number p- 3p -order sub- cycle group is weak 3 - DCI - group Shang-Wei Hsu Jin and PACKAGING 21-step sub- cycle group is not weak 3 - DCI - group of counter-examples are denied. In addition , Huang Qiongxiang given the Cayley subset is weak DCI- subset of the necessary and sufficient conditions , and prove that the dihedral group D 2n is a weak 2-DCI- group . The purpose of this paper is to continue the on the metacyclic group weak DCI- the research . Subset of the 5p order metacyclic group generated classification given in each category to generate a subset of DCI- sexual , and prove 5p order metacyclic group non- 5-DCI 's weak . Then , using a similar approach applied to the qp order metacyclic group , similar results can be obtained . In this paper, using group theory . The concept of group theory and algebraic graph theory References [1,2,3] .

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