The kk-Dominating Graph

Given a graph $G$, the $k$-dominating graph of $G$, $D_k(G)$, is defined to be the graph whose vertices correspond to the dominating sets of $G$ that have cardinality at most $k$. Two vertices in $D_k(G)$ are adjacent if and only if the corresponding dominating sets of $G$ differ by either adding or deleting a single vertex. The graph $D_k(G)$ aids in studying the reconfiguration problem for dominating sets. In particular, one dominating set can be reconfigured to another by a sequence of single vertex additions and deletions, such that the intermediate set of vertices at each step is a dominating set if and only if they are in the same connected component of $D_k(G)$. In this paper we give conditions that ensure $D_k(G)$ is connected.Comment: 2 figure, The final publication is available at http://link.springer.co

Turnaround Time Between ILLiad’s Odyssey and Ariel Delivery Methods: A Comparison

Interlibrary loan departments are frequently looking for ways to reduce turnaround time. The advent of electronic delivery in the past decade has greatly reduced turnaround time for articles, but recent developments in this arena have the potential to decrease that time even further. The ILLiad ILL management system has an electronic delivery component, Odyssey, with a Trusted Sender setting that allows articles to be sent to patrons without borrowing staff intervention, provided the lending library is designated as a Trusted Sender, or this feature is enabled for all lenders. Using the tracking data created by the ILLiad management system, the turnaround time for two delivery methods, Ariel and Odyssey, was captured for two different academic institutions. With the Trusted Sender setting turned on, Odyssey delivery was faster than Ariel for the institutions studied

Outer space for untwisted automorphisms of right-angled Artin groups

For a right-angled Artin group $A_\Gamma$, the untwisted outer automorphism group $U(A_\Gamma)$ is the subgroup of $Out(A_\Gamma)$ generated by all of the Laurence-Servatius generators except twists (where a {\em twist} is an automorphisms of the form $v\mapsto vw$ with $vw=wv$). We define a space $\Sigma_\Gamma$ on which $U(A_\Gamma)$ acts properly and prove that $\Sigma_\Gamma$ is contractible, providing a geometric model for $U(A_\Gamma)$ and its subgroups. We also propose a geometric model for all of $Out(A_\Gamma)$ defined by allowing more general markings and metrics on points of $\Sigma_\Gamma$.Comment: Example section added, introduction modified. Final version, to appear in Geometry and Topolog

An Historical - Geographical Survey of Vermilion County

Vermilion County is located in an area well favored with material resources and, because of this, was predestined to be an important part in the making of Illinois history. The county lies along the eastern border of Illinois, nearly midway in the state, generally between 40° -41° north latitude and 87° -88° west longitude. It is rectangular in shape, averaging 21.5 miles wide and 42 miles long, with an approximate area of 886 square miles. The following pages present a discussion of the natural resources of this area and a meager report on the struggles of those people involved in its development