Connected Domination Critical Graphs

This thesis investigates the structure of connected domination critical graphs. The characterizations developed provide an important theoretical framework for addressing a number of difficult computational problems in the areas of operations research (for example, facility locations, industrial production systems), security, communication and wireless networks, transportation and logistics networks, land surveying and computational biology. In these application areas, the problems of interest are modelled by networks and graph parameters such as domination numbers reflect the efficiency and performance of the systems

An Algebraic Exploration of Dominating Sets and Vizing's Conjecture

Systems of polynomial equations are commonly used to model combinatorial problems such as independent set, graph coloring, Hamiltonian path, and others. We formulate the dominating set problem as a system of polynomial equations in two di erent ways: rst, as a single, high-degree polynomial, and second as a collection of polynomials based on the complements of domination-critical graphs. We then provide a su cient criterion for demonstrating that a particular ideal representation is already the universal Gr obner bases of an ideal, and show that the second representation of the dominating set ideal in terms of domination-critical graphs is the universal Gr obner basis for that ideal. We also present the rst algebraic formulation of Vizing's conjecture, and discuss the theoretical and computational rami cations to this conjecture when using either of the two dominating set representations described above

Codiameters of 3-domination critical graphs with toughness more than one

Author name used in this publication: C. T. Ng2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Hamilton-connectivity of 3-domination critical graphs with α=δ+1≥5

Author name used in this publication: C. T. Ng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe