Document Type
Lecture
Publication Date
10-9-2009
Abstract
Let G be a graph such that each vertex of G is contained in a (k + 1)clique for a positive integer k. We de ne the shell of G, denoted by Sh(G) as follows: The vertex set of Sh(G) consists of all distinct (k + 1)-cliques of G and two vertices in Sh(G) are adjacent if and only if the corresponding (k +1)-cliques have k vertices in common. If k = 1, Sh(G) will be the line graph of G. If G is a k-tree with at least k + 1 vertices, each vertex of G is contained in a (k +1)-clique. In this talk, we will focus our attention on the shell of k-trees. Some properties and results on independence polynomials of the shells of k-trees will be presented and some related research problems will be proposed.
Relational Format
presentation
Recommended Citation
Staton, William, "On the shell of some graphs" (2009). Combinatorics Seminar. 79.
https://egrove.olemiss.edu/math_combinatorics/79
