|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||On graphs with an eigenvalue of maximal multiplicity|
Strongly regular graph
|Citation:||Rowlinson P (2013) On graphs with an eigenvalue of maximal multiplicity, Discrete Mathematics, 313 (11), pp. 1162-1166.|
|Abstract:||Let G be a graph of order n with an eigenvalue μ≠-1,0 of multiplicity k<n-2. It is known that k≤n+√2-2n+¼, equivalently k≤½t(t-1), where t=n-k>2. The only known examples with k=½t(t-1) are 3K2 (with n=6, μ=1, k=3) and the maximal exceptional graph G36 (with n=36, μ=-2, k=28). We show that no other example can be constructed from a strongly regular graph in the same way as G36 is constructed from the line graph L(K9).|
|Rights:||Published in Discrete Mathematics by Elsevier; Elsevier believes that individual authors should be able to distribute their accepted author manuscripts for their personal voluntary needs and interests, e.g. posting to their websites or their institution’s repository, e-mailing to colleagues. The Elsevier Policy is as follows: Authors retain the right to use the accepted author manuscript for personal use, internal institutional use and for permitted scholarly posting provided that these are not for purposes of commercial use or systematic distribution. An "accepted author manuscript" is the author’s version of the manuscript of an article that has been accepted for publication and which may include any author-incorporated changes suggested through the processes of submission processing, peer review, and editor-author communications.|
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