Spring 2006 M 690 I : Extremal Graph Theory Scribe : Ryan Martin

Lecture Notes Spring 2006 M 690 I : Extremal Graph Theory

Notes on Extremal Graph Theory

What you see below are notes related to a course that I have given several times in Extremal Graph Theory. I guarantee no accuracy with respect to these notes and I certainly do not guarantee completeness or proper attribution. This is an early draft and, with any luck and copious funding, some of this can be made into a publishable work and some will just remain as notes. Please do not distrib...

Edit Distance in Graphs

The focus of my research is extremal graph theory and random combinatorial structures. I have also worked in a variety of other areas, including intersecting hypergraphs, the theory of positional games and Ramsey theory. I use a number of tools in my research, notably probabilistic methods and, most prominently, Szemerédi’s regularity lemma. I have used these and other techniques to address que...

Ryan Martin

The focus of my research is extremal graph theory and random combinatorial structures. I have also worked in a variety of other areas, including intersecting hypergraphs, the theory of positional games and Ramsey theory. Combinatorics, and particularly graph theory, has a wide variety of applications. My own research in the edit distance of graphs has applications in biology and computer scienc...

The Signless Laplacian Estrada Index of Unicyclic Graphs

‎For a simple graph $G$‎, ‎the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$‎, ‎where $q^{}_1‎, ‎q^{}_2‎, ‎dots‎, ‎q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...