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Study on Some Types of the Lower Bounds of Domination Numbers in Graphs

Author: ZouXiaoLi
Tutor: ChenXueGang；LiuXiKui
School: Shandong University of Science and Technology
Course: Basic mathematics
Keywords: Control number Full symbolic control function Full control of the number of symbols Negative side control function Negative side control number Signed edge control function Signed edge domination number
CLC: O157.5
Type: Master's thesis
Year: 2008
Downloads: 28
Quote: 0
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Abstract


For Figure G = (V, E), a subset of S (?) V, said the point set S is a dominating set of G , if for any y ∈ VS, exists x ∈ S, so that xy ∈ E (G) . Because control theory has drawn increasing attention, the number of people on a deeper understanding of the control proposed different control number. For example: the number of symbolic control , signed edge domination number, total domination number of other symbols . These control the configuration in FIG number plays an important role. This paper mainly discusses several types of control chart number lower bound . In [ 3 ] , the Lu progress, Liu forest gives full control function is defined symbols , and gives some special graphs whole upper bound on the number of symbolic control . This figure continues to study full- signed domination number , and get some special graphs the lower bound of total signed domination number , followed by a general graph are given full control of the number of symbols lower bound . This article also gives a figure of negative side control definition: Let G be a graph, a function f: E → {-1,0,1} is called a graph G is a negative side control function, if f [e] = f (N [e]) = Σ x ∈ N [e] f (x) ≥ 1 for all edges e ∈ E holds. The negative side of the control graph G is defined as : γ e - (G) = min {f (E) | f is the negative side of the control graph G is a function } . And discussed the negative side of the control chart number lower bound , but also depicts the γ e - (G) = | E (G) | Fig. Finally, this paper studied the road signed edge domination number of circles , that gives the (?) ≤ γ se (P n ) ≤ (?).

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