Weakly Hadamard diagonalizable graphs

Adm, Mohammad; Almuhtaseb, Khawla; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla; Shirazi, Mahsa; Razafimahatratra, A. S.

dc.contributor.author	Adm, Mohammad
dc.contributor.author	Almuhtaseb, Khawla
dc.contributor.author	Fallat, Shaun
dc.contributor.author	Meagher, Karen
dc.contributor.author	Nasserasr, Shahla
dc.contributor.author	Shirazi, Mahsa
dc.contributor.author	Razafimahatratra, A. S.
dc.date.accessioned	2021-05-04T07:59:21Z
dc.date.accessioned	2022-05-22T08:54:38Z
dc.date.available	2021-05-04T07:59:21Z
dc.date.available	2022-05-22T08:54:38Z
dc.date.issued	2021-02-01
dc.identifier.issn	0024-3795
dc.identifier.uri	http://localhost:8080/xmlui/handle/123456789/8306
dc.description.abstract	A matrix is called weakly Hadamard if its entries are from {0, -1, 1} and its non-consecutive columns (with some ordering) are orthogonal. Unlike Hadamard matrices, there is a weakly Hadamard matrix of order n for every n>= 1. In this work, graphs for which their Laplacian matrices can be diagonalized by a weakly Hadamard matrix are studied. A number of necessary and sufficient conditions are verified along with identification of numerous families of graphs whose Laplacian matrices can be diagonalized by a weakly Hadamard matrix.	en_US
dc.description.sponsorship	The work in this paper was a joint project of the Discrete Mathematics Research Group at the University of Regina, attended by all of the authors. Dr. Fallat's research was supported in part by NSERC Discovery Research Grant, Application No.: RGPIN-2019-03934. Dr. Meagher's research was supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-03952-2018. Dr. Nasserasr's research was supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2019-05275	en_US
dc.language.iso	en	en_US
dc.publisher	Linear Algebra and its Applications Journal	en_US
dc.subject	Hadamard matrices	en_US
dc.subject	Laplacians	en_US
dc.subject	Eigenspaces	en_US
dc.subject	Strongly-regular graphs	en_US
dc.title	Weakly Hadamard diagonalizable graphs	en_US
dc.type	Article	en_US