Weakly Chordal Graphs: An Experimental Study

Graph theory is an important field that enables one to get general ideas about graphs and their properties. There are many situations (such as generating all linear layouts of weakly chordal graphs) where we want to generate instances to test algorithms for weakly chordal graphs. In my thesis, we address the algorithmic problem of generating weakly chordal graphs. A graph G=(V, E), where V is its vertices and E is its edges, is called a weakly chordal graph, if neither G nor its complement G\u27, contains an induced chordless cycle on five or more vertices. Our work is in two parts. In the first part, we carry out a comparative study of two existing algorithms for generating weakly chordal graphs. The first algorithm for generating weakly chordal graphs repeatedly finds a two-pair and adds an edge between them. The second-generation algorithm starts by constructing a tree and then generates an orthogonal layout (also weakly chordal graph) based on this tree. Edges are then inserted into this orthogonal layout until there are $m$ edges. The output graphs from these two methods are compared with respect to several parameters like the number of four cycles, run times, chromatic number, the number of non-two-pairs in the graphs generated by the second method. In the second part, we propose an algorithm for generating weakly chordal graphs by edge deletions starting from an arbitrary input random graph. The algorithm starts with an arbitrary graph to be able to generate a weakly chordal graph by the basis of edge deletion. The algorithm iterates by maintaining weak chordality by preventing any hole or antihole configurations being formed for any successful deletion of an edge