Zobrazeno 1 - 10
of 11
pro vyhledávání: '"Carolyn Reinhart"'
Publikováno v:
The Electronic Journal of Linear Algebra. 36:744-763
A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distanc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d638cce66f4f937ac581769cd7715a78
https://doi.org/10.13001/ela.2020.5243
https://doi.org/10.13001/ela.2020.5243
Autor:
Leslie Hogben, Carolyn Reinhart
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs -- a 2014 survey by Aouchiche and Hansen on spectra of di
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::36adfba05ecfda9e7d3af4577406b62f
Publikováno v:
University of Wyoming Open Journals
A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the distance matrix, distance Laplacian, and distance signless Laplacian, in addition
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c08d2b9d87330d5542c70ce9efad9d9
http://arxiv.org/abs/2003.03412
http://arxiv.org/abs/2003.03412
Publikováno v:
Discrete Mathematics. 341:2418-2430
We consider the cop-throttling number of a graph G for the game of Cops and Robbers, which is defined to be the minimum of ( k + capt k ( G ) ) , where k is the number of cops and capt k ( G ) is the minimum number of rounds needed for k cops to capt
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ddc2d87b11f79d8556db6ee4e2736f8b
https://doi.org/10.1016/j.disc.2018.05.017
https://doi.org/10.1016/j.disc.2018.05.017
Autor:
Carolyn Reinhart
Publikováno v:
Special Matrices, Vol 9, Iss 1, Pp 1-18 (2021)
The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of tra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7feb6b7f0bbc19c5faafa7e3339376c8
http://arxiv.org/abs/1903.04575
http://arxiv.org/abs/1903.04575
Autor:
Anthony Bonato, Jane Breen, Boris Brimkov, Joshua Carlson, Sean English, Jesse Geneson, Leslie Hogben, K. E. Perry, Carolyn Reinhart
The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber on $G$ ov
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6bc0f4331f990780df864d207edc3cf2
Autor:
Leslie Hogben, Kate Lorenzen, Mark Yarrow, Carolyn Reinhart, Boris Brimkov, Ken Duna, Sung-Yell Song
Publikováno v:
The Electronic Journal of Linear Algebra
The distance matrix $\mathcal{D}(G)$ of a graph $G$ is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is $\mathcal{D}^L(G)=T(G)-\mathcal{D}(G)$, where $T(G)$ is the diagonal matrix of row sums of $\ma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a570142c3c5d0c2c0aade7037e209c84
http://arxiv.org/abs/1812.05734
http://arxiv.org/abs/1812.05734
Autor:
Boris Brimkov, Rachel Kirsch, Michael Phillips, Ariel Keller, Kirk Boyer, Carolyn Reinhart, Daniela Ferrero, Sean English
Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to become colored. A zero forcing set is a set of initially colored vertices
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45a9a3c13cabcfe3e40b82a8c545022b
http://arxiv.org/abs/1801.08910
http://arxiv.org/abs/1801.08910
Publikováno v:
Involve 10, no. 5 (2017), 767-779
Given a graph [math] , the tree cover number of the graph, denoted [math] , is the minimum number of vertex disjoint simple trees occurring as induced subgraphs that cover all the vertices of G. This graph parameter was introduced in 2011 as a tool f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a559939ce995e8415f1aff3119887532
https://projecteuclid.org/euclid.involve/1508433091
https://projecteuclid.org/euclid.involve/1508433091