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Zeta function on the finite graph

Author: ZhouXueLian
Tutor: LiKeZheng；YangZiFeng
School: Capital Normal University
Course: Basic mathematics
Keywords: edge matrix loop zeta function
CLC: O157.5
Type: Master's thesis
Year: 2009
Downloads: 18
Quote: 0
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Abstract


We consider the element discussion of Ihara-type zeta function and their generalization for finite,possibly irregular graphs.Given a finite graph,there is a group at every vertex.The group may be a finite group（order＞1） not necessarily be an unitary group.Then the definition of loop has been changed. In this paper,we will adapt the definition of loop of（G,X） and calculate the number of non-backtracking,tailless loops.Then we will give out two definitions:The first is more simply,we define an equivalent class over the above loop, eg.two cycles C=ay1y2y3 and D=y1y2y3a,we say C～D.In this case,zeta function is a real function.The second definition is a directed generalization of Ihara zeta functions.In other words,Ihara zeta functions is its special case.For the more,we will give some explicit examples of zeta functions for finite graph.

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