Zu-hua Liao

Bio: Zu-hua Liao is an academic researcher from Jiangnan University. The author has contributed to research in topics: Type (model theory) & Projection (relational algebra). The author has an hindex of 1, co-authored 5 publications receiving 1 citations.

(a, b)-Roman Domination on Cacti

Abstract: Given two real numbers \(b\ge a>0\), an (a, b)-Roman dominating function on a graph \(G=(V,E)\) is a function \(f:V\rightarrow \{0,a,b\}\) satisfying the condition that every vertex v for which \(f(v)=0\) is adjacent to a vertex u for which \(f(u)=b\). In the present paper, we design a linear-time algorithm to produce a minimum (a, b)-Roman dominating function for cacti, a superclass of trees and different from chordal graphs.

A New Type Soft Prime Ideal of KU-algebras

Abstract: Through combining the soft set with KU-algebras, this paper introduces the concept of a new type soft prime ideal of KU-algebras and investigates its properties. Firstly, we give the equivalent descriptions of the new type prime soft ideal of KU-algebras. Then, we show the differences between the new type soft prime ideal of KU-algebras and the common soft prime ideal of KU-algebras by giving examples. After then, studies about the equivalent description of the new type soft prime ideal and the new type soft ideal prove that the algebraic structure of dual soft set is different from the algebraic structure of \(\alpha \)-level set. Besides, we define the new concept of the projection of AND operation of soft set, and the obtain that the projection of AND operation of two soft set is also the new type soft prime ideal, if the AND operation is a new type soft prime ideal of KU-algebras. Finally, we explore the properties of the new type soft prime ideal of KU-algebras about the image and inverse image.

The \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) -\) fuzzy Subalgebras of \(KU -\) algebras

Abstract: In this paper, we carry out a detailed investigation into the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra of a \(KU - \) algebra from the following aspects. Firstly, the concepts of the pointwise \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra and generalized fuzzy subalgebra of KU-algebras are introduced. Secondly, the equivalent descriptions of the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra are given, including the level set, the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra is better than \(( \in , \in ) - \) fuzzy subalgebra and \(( \in , \in \vee q) - \) fuzzy subalgebra, which has rich hierarchy structure. Once more, we use methods of pointwise to discuss some basic properties of homomorphic image and homomorphic preimage of the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra. Finally, we discuss the related properties about direct product and projection.

On \((\in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras

Abstract: First, new concepts of pointwise \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals and generalized fuzzy ideals of KU-algebras are defined. By using inequalities, level sets and characteristic functions, some equivalent characterizations of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are studied, a richer hierarchical structure of this fuzzy ideal is presented, and some properties are discussed using the partial order of KU-algebras. Second, it is proven that the intersections, unions (under certain conditions), homomorphic image and homomorphic preimage of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are also \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals. Then, the direct product and projection of the \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are also investigated. Finally, a new concept of the descending (ascending) chain conditions of the ideals of KU-algebras is introduced and is studied using the properties of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals.

On Derivations of FI-Algebras

Abstract: In this paper, firstly, the concept of a new type of derivations on FI-algebras is introduced. The existence of it is verified by an example and a program. Then, the concepts of different kinds of derivations on FI-algebras are given. The properties of derivations on FI-algebras and the relationship between derivations and ideal are investigated. The equivalent conditions of identity derivation and the equivalent conditions of isotone derivation are proved. Finally, the concept of \(a-\)principal derivations on DFI-algebras is given. The existence of \(a-\)principal derivations is verified by an example and a program.

Efficient algorithms for Roman domination on some classes of graphs

Abstract: A Roman dominating function of a graph G=(V,E) is a function f:V->{0,1,2} such that every vertex x with f(x)=0 is adjacent to at least one vertex y with f(y)=2. The weight of a Roman dominating function is defined to be f(V)=@?"x"@?"Vf(x), and the minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this paper we first answer an open question mentioned in [E.J. Cockayne, P.A. Dreyer Jr., S.M. Hedetniemi, S.T. Hedetniemi, Roman domination in graphs, Discrete Math. 278 (2004) 11-22] by showing that the Roman domination number of an interval graph can be computed in linear time. We then show that the Roman domination number of a cograph (and a graph with bounded cliquewidth) can be computed in linear time. As a by-product, we give a characterization of Roman cographs. It leads to a linear-time algorithm for recognizing Roman cographs. Finally, we show that there are polynomial-time algorithms for computing the Roman domination numbers of AT-free graphs and graphs with a d-octopus.