TY - JOUR

T1 - Understanding the properties of isospectral points and pairs in graphs

T2 - The concept of orthogonal relation.

AU - Rücker, Christoph

AU - Rücker, Gerta

PY - 1992/9

Y1 - 1992/9

N2 - The mathematical property "orthogonal relationship" is used in proving the fact that isospectrality, isocodality and isocoefficiency of vertices within a graph are all equivalent. The same is true for isospectrality, "strict isocodality" and "strict isocoefficiency" of pairs (including edges) within a graph, whereas the "weak" versions of the latter properties are necessary but not sufficient for isospectrality of pairs. Similarly, necessary and sufficient conditions for isospectrality of vertices and pairs in different graphs are derived. In all these proofs, the concept of "orthogonal relation" plays a major role in that it allows the use of tools of elementary linear algebra.

AB - The mathematical property "orthogonal relationship" is used in proving the fact that isospectrality, isocodality and isocoefficiency of vertices within a graph are all equivalent. The same is true for isospectrality, "strict isocodality" and "strict isocoefficiency" of pairs (including edges) within a graph, whereas the "weak" versions of the latter properties are necessary but not sufficient for isospectrality of pairs. Similarly, necessary and sufficient conditions for isospectrality of vertices and pairs in different graphs are derived. In all these proofs, the concept of "orthogonal relation" plays a major role in that it allows the use of tools of elementary linear algebra.

KW - Chemistry

UR - http://www.scopus.com/inward/record.url?scp=0001478710&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/8fb66a2e-ce9a-3140-8323-9da8303d4d8a/

U2 - 10.1007/BF01165148

DO - 10.1007/BF01165148

M3 - Journal articles

VL - 9

SP - 207

EP - 238

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 3

ER -