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Upper Minus Domination Number of Regular Graphs

Author: ZhaoHongTao
Tutor: LvXinZhong
School: Zhejiang Normal University
Course: System theory
Keywords: Cubic Four regular Five regular k- regular Less control number Reduce the number of edge control
CLC: O157.5
Type: Master's thesis
Year: 2010
Downloads: 19
Quote: 0
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Abstract


Figure G = (V, E) on the function f: V → {-1,0,1} is called a graph G is a reduction on the control function, if for any point v ∈ V, have less control function f is a minimal reduction of G on the control function , if there is less control function g: V → {-1,0,1}, f ≠ g, such that for any point v ∈ V, g (v) ≤ f (v) are set . decrement the number of G is usually expressed as γ-(G), which is G all the weight reduction control function of the smallest value among ; FIG upper decrement the number of G denoted Γ-(G ) , which is a graph G minimal reduction control all the functions of the maximum value among the weight . that is, : γ-(G) = min {ω (f) | f is less control functions on G } and Γ- (G) = max {ω (f) | f is G minus control function on minimal } Figure G = (V, E) on the function f: E → {-1,0,1} is known to be Save on the side of G control function, if for every edge of G e ∈ E has less side control of G number of usually expressed as γ'm (G), which is a reduction of G on all sides control Functions the smallest value among the weight ; reduction in the Upper edges of G is denoted by the number of control Γ'm (G), which is all the small graph G minus side control functions among the maximum value of the weight . that is, : γ- (G) = min {ω (f) | f is G control functions on the minus side } and Γ-(G) = max {ω (f) | f is G minus side on the tiny control function } in this paper, for the analysis of structural properties of graphs obtained regular graphs Upper minus domination number , the main conclusions are as follows : ( a ) for any cubic graph G of order n has Γ-(G) ≤ 5/8n, and this sector is reachable and construct a class of Γ-(G) = 5/8n diagram ; for any order n four regular graph G has a Γ-(G) ≤ 7 / (10) n; for any order n five regular graph G has a Γ-(G) ≤ 3/4n; (2) for any n -order k- regular graph G has a Γ-(G) ≤ (2k-1) / (2 (k 1)) n; (3) for any of the tri-n with m edges then G has Γ'm (G) ≤ (2m) / 3.

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