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Full-Text Articles in Logic and Foundations
Conjugacy Separability And Cyclic Conjugacy Separability Of Certain Hnn Extensions, Generalised Free Products And Tree Products, Hui Min Lim
Student Works (2020-2029)
In this thesis, we study two interrelated strong residually finite properties of groups, namely conjugacy separability and cyclic conjugacy separability. We extend them to certain HNN extensions, generalized free products and tree products where the associated subgroups and amalgamated subgroups are not necessarily cyclic. In the first part of the thesis, we consider HNN extensions. We begin by establishing two criteria, one for conjugacy separability and another for cyclic conjugacy separability. Using these two criteria we establish conditions for HNN extensions where the associated subgroups are central or they are a finite extension of a central subgroup or cyclic to …
On Self-Clique Graphs., Ong Poh Hwa
On Self-Clique Graphs., Ong Poh Hwa
Student Works (2010-2019)
The clique graph of a graph G is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques have non-empty intersection. A graph G is self-clique if it is isomorphic to its clique graph. Clique graphs have been studied for some time. However, not much is known about self-clique graphs. Self-clique graphs were ¯rst introduced and studied by Escalante [Abh. Math. Sem. Univ. Hamburg 39 (1973) 59-68]. Since then, self-clique graphs have been characterized for some classes of graphs. Chia [Discrete Math. 212 (2000) 185-189] gave a …
On Minimal Regular Graphs With Given Constraintsm, Che Sheng Gan
On Minimal Regular Graphs With Given Constraintsm, Che Sheng Gan
Student Works (2000-2009)
A classical question in graph theory has been the search of cages. The problem of determining the smallest (r,g)-cage is unsolved for most pairs of (r,g) and is extremely hard in the general case. Finding the crossing number of a graph is another challenging problem in graph theory. The crossing numbers of very few classes of graphs arc known. In this thesis, we would like to (a) investigate those smallest regular graphs with given girths and having small crossing numbers. In particular, we investigate those smallest regular graphs with given girths and crossing number c, for c ∈ {0, 1, …
On Strongly N-Regular And Strongly Regular Rings, Huey Voon Chen
On Strongly N-Regular And Strongly Regular Rings, Huey Voon Chen
Student Works (2000-2009)
Let R be an associative ring with identity 1 (not equal to) 0. An element x E R is said to be right (or left) regular if there exists yin R such that x² y = x (or y.x² = x). If x is both left and right regular, then it is said to be strongly regular. The ring R is said to be strongly regular if every element of R is strongly regular. We say that x is a left -π-regular element if there exist an integer n > 0 and an element y E R such that yx n+1 …