Graphs defined by orthogonality

B. R. Bakhadly; A. E. Guterman; O. V. Markova

doi:10.1007/s10958-015-2393-6

Graphs defined by orthogonality

B. R. Bakhadly, A. E. Guterman, O. V. Markova

Research output: Contribution to journal › Article › peer-review

Abstract

The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced. The main attention is paid to the commutative rings and to the matrix ring over a field and its various subrings and subsets. In particular, the diameters of the orthogonality graphs of the full matrix algebra over an arbitrary field and its subsets consisting of diagonal, diagonalizable, triangularizable, and nilpotent matrices are computed. Bibliography: 36 titles.

Original language	English
Pages (from-to)	698-717
Number of pages	20
Journal	Journal of Mathematical Sciences
Volume	207
Issue number	5
DOIs	https://doi.org/10.1007/s10958-015-2393-6
State	Published - Jun 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Applied Mathematics

Access to Document

10.1007/s10958-015-2393-6

Cite this

@article{d7c83c3ffc524e6db2297bd87eb7862e,

title = "Graphs defined by orthogonality",

abstract = "The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced. The main attention is paid to the commutative rings and to the matrix ring over a field and its various subrings and subsets. In particular, the diameters of the orthogonality graphs of the full matrix algebra over an arbitrary field and its subsets consisting of diagonal, diagonalizable, triangularizable, and nilpotent matrices are computed. Bibliography: 36 titles.",

author = "Bakhadly, \{B. R.\} and Guterman, \{A. E.\} and Markova, \{O. V.\}",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

year = "2015",

month = jun,

doi = "10.1007/s10958-015-2393-6",

language = "الإنجليزيّة",

volume = "207",

pages = "698--717",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Science and Business Media Deutschland GmbH",

number = "5",

}

TY - JOUR

T1 - Graphs defined by orthogonality

AU - Bakhadly, B. R.

AU - Guterman, A. E.

AU - Markova, O. V.

PY - 2015/6

Y1 - 2015/6

N2 - The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced. The main attention is paid to the commutative rings and to the matrix ring over a field and its various subrings and subsets. In particular, the diameters of the orthogonality graphs of the full matrix algebra over an arbitrary field and its subsets consisting of diagonal, diagonalizable, triangularizable, and nilpotent matrices are computed. Bibliography: 36 titles.

AB - The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced. The main attention is paid to the commutative rings and to the matrix ring over a field and its various subrings and subsets. In particular, the diameters of the orthogonality graphs of the full matrix algebra over an arbitrary field and its subsets consisting of diagonal, diagonalizable, triangularizable, and nilpotent matrices are computed. Bibliography: 36 titles.

UR - http://www.scopus.com/inward/record.url?scp=84949623888&partnerID=8YFLogxK

U2 - 10.1007/s10958-015-2393-6

DO - 10.1007/s10958-015-2393-6

M3 - مقالة

SN - 1072-3374

VL - 207

SP - 698

EP - 717

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 5

ER -

Graphs defined by orthogonality

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this