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Research on the Sequence of a Class of Graphs

Author: RenHongJie
Tutor: XuMeiJin
School: Liaoning University of Technology
Course: Applied Mathematics
Keywords: Labeling sequential labeling sequence of odd cycle even cycle
CLC: O157.5
Type: Master's thesis
Year: 2014
Downloads: 6
Quote: 0
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Graph theory is an important branch of combinatorial mathematics, they are used inradio astronomy, X-ray diffraction crystallography, cryptography, communication networkcoding field access, missile control code design, code design of synchronous machine.Graph labeling traces its origin to the1966A. Rosa’s famous guess of graceful trees. Agraph labeling is the vertex set of a graph map to integer set. According to the differentrequirement for the mapping, it produced a variety of graph labeling problem. The concept ofsequential labeling is1980, Chang, Hsu and Grace in harmonious labeling solution errorcorrecting code, examine the harmonic sub-graph is proposed, by labeling a harmoniouslabeling derived.The thesis firstly introduces the research background of the problem graph, and brieflyintroduces the research development of graceful graphs, harmony, balance and other types oflabel, emphatically introduces the research status of sequential labeling of graphs, and showthe relationship between a few class labeling. At the same time, this thesis discusses someproperties of the sequence diagram, and introduces a graph of the sequence of severalsufficient, necessary and sufficient and necessary conditions. We can construct the sequencelabeling the different use of these theories, to judge whether a graph is a sequence diagram.Do not pay and diagram of the sequence of this thesis focuses on the odd circle and evencycles, consider the study of the structural similarity between graphs with odd circle, wastransformed by sequential labeling odd circle on the existing annotation methods, wedeveloped a method of a class label to study. As a result of the general bipartite graphC2kinthis class, the value of K is analyzed, which is divided into four categories: k=4m,k=4m+1,k=4m+2,k=4m+3. In the different values of K, discusses respectively according to theparity of m, It obtained the sequence labeling of this kind of graphsC7∪C2k, and gives astrict mathematical proof.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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