On strongly regular graphs with m2 = qm3 and m3 = qm2

• Volume: 37, Issue: 4, page 353-364
• ISSN: 1310-6600

top

Abstract

top
2010 Mathematics Subject Classification: 05C50.We say that a regular graph G of order n and degree r і 1 (which is not the complete graph) is strongly regular if there exist non-negative integers t and q such that |SiЗSj| = t for any two adjacent vertices i and j, and |SiЗSj| = q for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let l1 = r, l2 and l3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, l2 and l3, respectively. We here describe the parameters n, r, t and q for strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 2, 3, 4.

How to cite

top

Lepovic, Mirko. "On strongly regular graphs with m2 = qm3 and m3 = qm2." Serdica Mathematical Journal 37.4 (2011): 353-364. <http://eudml.org/doc/281562>.

@article{Lepovic2011,
abstract = {2010 Mathematics Subject Classification: 05C50.We say that a regular graph G of order n and degree r і 1 (which is not the complete graph) is strongly regular if there exist non-negative integers t and q such that |SiЗSj| = t for any two adjacent vertices i and j, and |SiЗSj| = q for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let l1 = r, l2 and l3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, l2 and l3, respectively. We here describe the parameters n, r, t and q for strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 2, 3, 4.},
author = {Lepovic, Mirko},
journal = {Serdica Mathematical Journal},
keywords = {Strongly Regular Graph; Conference Graph; Integral Graph; strongly regular graph; conference graph; integral graph},
language = {eng},
number = {4},
pages = {353-364},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On strongly regular graphs with m2 = qm3 and m3 = qm2},
url = {http://eudml.org/doc/281562},
volume = {37},
year = {2011},
}

TY - JOUR
AU - Lepovic, Mirko
TI - On strongly regular graphs with m2 = qm3 and m3 = qm2
JO - Serdica Mathematical Journal
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 37
IS - 4
SP - 353
EP - 364
AB - 2010 Mathematics Subject Classification: 05C50.We say that a regular graph G of order n and degree r і 1 (which is not the complete graph) is strongly regular if there exist non-negative integers t and q such that |SiЗSj| = t for any two adjacent vertices i and j, and |SiЗSj| = q for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let l1 = r, l2 and l3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, l2 and l3, respectively. We here describe the parameters n, r, t and q for strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 2, 3, 4.
LA - eng
KW - Strongly Regular Graph; Conference Graph; Integral Graph; strongly regular graph; conference graph; integral graph
UR - http://eudml.org/doc/281562
ER -

NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.