Discrete Mathematics

1986 ◽  
pp. 31-48
Author(s):  
Renfrey B. Potts
Keyword(s):  
Discrete Mathematics

Learning Discrete Mathematics with ISETL

1989 ◽  
Author(s):  
Nancy Baxter ◽  
Ed Dubinsky ◽  
Gary Levin
Keyword(s):  
Discrete Mathematics

scholarly journals Quadruple Roman Domination in Trees

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1318
Author(s):  
Zheng Kou ◽  
Saeed Kosari ◽  
Guoliang Hao ◽  
Jafar Amjadi ◽  
Nesa Khalili
Keyword(s):  
Open Neighborhood ◽  
Minimum Weight ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Upper And Lower Bounds ◽  
Discrete Mathematics ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Vertex Set ◽  
Roman Dominating Function

This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)<k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.

scholarly journals From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1036
Author(s):  
Abel Cabrera Martínez ◽  
Alejandro Estrada-Moreno ◽  
Juan Alberto Rodríguez-Velázquez
Keyword(s):  
Vertex Cover ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Special Issue ◽  
Total Domination Number ◽  
Theoretical Computer ◽  
Graph Parameters ◽  
Semitotal Domination ◽  
Domination In Graphs

This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x∈V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X⊆V(G) is defined to be N(X)=⋃x∈XN(x), while the external neighbourhood of X is defined to be Ne(X)=N(X)∖X. Now, for every set X⊆V(G) and every vertex x∈X, the external private neighbourhood of x with respect to X is defined as the set Pe(x,X)={y∈V(G)∖X:N(y)∩X={x}}. Let Xw={x∈X:Pe(x,X)≠⌀}. The strong differential of X is defined to be ∂s(X)=|Ne(X)|−|Xw|, while the quasi-total strong differential of G is defined to be ∂s*(G)=max{∂s(X):X⊆V(G)andXw⊆N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.

scholarly journals Resonance overvoltage control algorithms in long cable frequency conversion drive based on discrete mathematics

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 408-418
Author(s):  
Yonghong Deng ◽  
Quanzhu Zhang
Keyword(s):  
Mathematical Model ◽  
Control Strategy ◽  
Frequency Conversion ◽  
Balance Control ◽  
Frequency Converter ◽  
Active Power ◽  
Drive System ◽  
Discrete Mathematics ◽  
Power Controller ◽  
Capacitor Voltage

AbstractIn order to solve the problem that the long cable variable voltage and variable frequency (VVVF) system does not adopt an effective capacitor voltage sharing control method, resulting in a poor effect of resonance overvoltage control, the resonance overvoltage control algorithm of the long cable VVVF system based on discrete mathematics is studied. First, the long cable frequency conversion drive system is established. In order to ensure voltage loss in the range of motor requirements, a frequency converter–cable–motor (ICM) system connection mode is used to maintain the system operation. Based on the research of the capacitor voltage balance control strategy of a long cable frequency conversion drive system, the discrete mathematical model of the AC side of the ICM system is established by using this control strategy. The improved constant active power controller is obtained by establishing the mathematical model, and the resonant overvoltage in a long cable frequency conversion drive is realized by using the constant active power controller. The experimental results show that the algorithm can effectively control the resonance overvoltage phenomenon in the long cable frequency control system, and the control accuracy is over 97%. It has good performance and can be applied in practice.

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