Independence Number: Theory and Applications I.
Chair:
Craig Larson (Virginia Commonwealth University)
Org:
Ermelinda DeLaVina (University of HoustonDowntown) and
Craig Larson (Virginia Commonwealth University)
[
PDF]
 ERMELINDA DELAVINA, University of HoustonDowntown
Graffiti.pc on Independence [PDF]

Graffiti.pc is a graph theoretical conjecturemaking program whose creation was inspired by the wellknown program of Siemion Fajtlowicz, Graffiti. In addition to a brief description of the principles of the program we discuss Graffiti.pc's conjectured bounds on the independence number and other independence related graph invariants.
 ART FINBOW, Saint Mary's University
On WellCovered Planar Triangulations [PDF]

A graph G is said to be \textit{wellcovered} if every maximal independent set of vertices has the same cardinality. A planar (simple) graph in which each face is a triangle is called a \textit{triangulation}. A characterization of the planar wellcovered triangulations has finally been completed. In a series of three previous papers, we have completed the 4 and 5connected cases. This talk will focus on the 3connected case.
This is joint work with B. L. Hartnell, R. Nowakowski and Michael D. Plummer.
 MICHAEL D. PLUMMER, Vanderbilt University
A Problem On Wellcovered Graphs [PDF] [SLIDES]

A graph is \textit{wellcovered} if every maxim\textit{al} independent set of vertices is also maxim\textit{um}. In other words, all maximal independent sets of vertices in the graph have the same cardinality.
I will present and discuss the recently solved problem of characterizing all wellcovered quadrangulations of the plane.
This is joint work with Finbow and Hartnell.
 WILLIAM STATON, University of Mississippi
Independence Polynomials of kTrees [PDF] [SLIDES]

Explicit formulas are known for the independence polynomials of several classes of trees. We discuss extensions of some of these formulas to the corresponding classes of ktrees. Additionally, we generalize, to ktrees, Wingardâ€™s bounds for the coefficients of the independence polynomial of a tree.
 DAVID TANKUS, Ariel University Center of Samaria, ISRAEL
Weighted WellCovered Graphs without Cycles of Lengths 4, 5, and 6 [PDF] [SLIDES]

A graph $G$ is \textit{wellcovered} if all its maximal independent sets are
of the same cardinality. Assume that a weight function $w$ is defined on its
vertices. Then $G$ is $w$\textit{wellcovered} if all maximal independent
sets are of the same weight. For every graph $G$, the set of weight functions
$w$ such that $G$ is $w$wellcovered is a \textit{vector space}. Given an
input graph $G$ without cycles of length $4$, $5$, and $6$, we characterize
polynomially the vector space of weight functions $w$ for which $G$ is $w$wellcovered.
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This is joint work with Vadim E. Levit.