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Pebbling in Split Graphs

Description

Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of

Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter 2 graphs, and that deciding whether the pebbling number has a prescribed upper bound is Π[P over 2]-complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guarantee it, with no characterization in sight. In this paper we investigate an important family of diameter 3 chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(n[superscript β]) time, where β = 2ω/(ω + 1) [= over ∼] 1.41 and ω [= over ∼] 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.

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Date Created
2013-11-30

Japanese-American Internment Camp Collection

Description

A presentation describing technical work, community reaction and publicity associated with an online collection of Arizona Japanese-American internment camp newsletters and related archival materials developed in 2017. The presentation was given at the Arizona Library Association conference in October 2017

A presentation describing technical work, community reaction and publicity associated with an online collection of Arizona Japanese-American internment camp newsletters and related archival materials developed in 2017. The presentation was given at the Arizona Library Association conference in October 2017 and this revised version was presented at the Arizona Archives Summit on February 1, 2018.

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Date Created
2018-01-18

Phoenix Annexation Workshop

Description

Materials produced for the workshop hosted by the Humane Cities Initiative, Institute for Humanities Research, Arizona State University. Participants were sent this package of archival materials and links to brief online sources for advance readings. Also enclosed are PDF renderings

Materials produced for the workshop hosted by the Humane Cities Initiative, Institute for Humanities Research, Arizona State University. Participants were sent this package of archival materials and links to brief online sources for advance readings. Also enclosed are PDF renderings of introductory powerpoint files by Spindler and Pagan, and an audio recording of the discussion joined in progress.

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Date Created
2018-03-13

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ASU in the Postwar Period: Victory Village

Description

Presentation slides regarding the history of Victory Village, the trailer park built in 1945-46 to provide housing for WWII Veterans and their families at Arizona State University's Tempe campus. A presentation of research from University Archives records conducted in the

Presentation slides regarding the history of Victory Village, the trailer park built in 1945-46 to provide housing for WWII Veterans and their families at Arizona State University's Tempe campus. A presentation of research from University Archives records conducted in the summer of 2018. The presentation was videotaped as a lecture for Professor Volker Benkert's online World War II history class.

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Date Created
2019-09-30

In Search of Strategic Direction: Digital Preservation in the Academy

Description

Video recording of the NHPRC Electronic Records Fellowship Symposium keynote address, University of North Carolina at Chapel Hill, November 18, 2005.

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Date Created
2005-11-18

ROTC Building Occupation at ASU, April 23-25, 1969

Description

Historical research produced for a portion of the exhibit entitled Civil Rights in Arizona, which was displayed at the Luhrs Gallery, Hayden Library in 2012-2013. The action at the ROTC Building was one of the largest protests in Arizona State

Historical research produced for a portion of the exhibit entitled Civil Rights in Arizona, which was displayed at the Luhrs Gallery, Hayden Library in 2012-2013. The action at the ROTC Building was one of the largest protests in Arizona State University history, resulting in the arrest of ten individuals. The second file, entitled "Who Were the Tempe Ten?", describes the arrested students and unaffiliated persons.

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2012

Selling Sunshine: ASU Solar Energy Research 1951-1980

Description

Original exhibit panel text and an associated interview with ASU faculty Charles Backus and Harvey Bryan for the exhibit presented at the Luhrs Gallery, Hayden Library, Fall, 2013.

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Created

Date Created
2013-07-01