Construction of strongly regular graphs using affine
Recommend Documents
Nov 24, 2014 - CO] 24 Nov 2014. Strongly Regular Graphs as Laplacian Extremal Graphs. Fan-Hsuan Linâ â . Chih-wen Wengâ . November 25, 2014. Abstract.
Nov 15, 2015 - A graph with only integer eigenvalues is termed an integral graph. ... We also provide some figures and examples of constructed graphs. ..... n(G, H) is a regular graph for all n. Proof. Suppose that Tr m(G, H) is regular where .... is
Apr 19, 1999 - In [Duv-88] the notion of srg's was generalized to directed graphs. ..... Lemma 5.10 Let D = (P,B,F) is a finite generalized quadrangle of order (s, ...
regular graph, which is traditionally called a group divisible (G.D.) asso- ... design, mdivides kand each block containsk/m treatments from each set. Si(i= 1,2, ...
ther, we construct two block designs, a 2-(65, 15, 21) design and a 2-. (65, 26 ..... PG(2, 16). A setwise stabilizer in Aut(D1) of a union of three disjoint blocks.
Note that if a parameter set is feasible for a spread, then so is the parameter set of the complement. Hoffman ... Then F has chromatic number 3 and F is the Lattice graph L(3). (i.e. the line ...... T.H.-Report 76-WSK-01, Techn. Univ. Eindhoven ...
Oct 26, 2004 - is a 3 -regular graph on 2¿ vertices, consider its outer boundary. Let ... (Dotted lines are deleted). Figure 2 : ( 9 ,4) graph. If ¿ = 2 t + 1, we must have t > 2 since q5 is not planar. First ... T his will give a 4-regular planar
Jan 3, 2012 - uniform cyclotomy, which will be defined in Section 2. .... semi-primitive case (also referred to as uniform cyclotomy or pure Gauss sum), where ...
Jan 27, 2014 - CO] 27 Jan 2014. Strongly Regular Graphs With The 7-Vertex ..... Theorem 6 (Cameron [10]). The point graph of a generalised quadrangle ...
Oct 5, 2017 - show that, for every strongly regular graph, there is some ... known distance regular graphs [9], where perfect state transfer in strongly regular ...
Mar 9, 2006 - a strongly regular locally GQ(s, t) graph in which every µ-subgraph is ... quotient of the Johnson graph J(10, 5), or s = t = 1, 2, 3, 8, 13; (2) â is a ...
Feb 11, 2010 - ... due to several applications in mathematical finance, where they ...... Applying the tower law (N â 1)-times in the same way (conditioning on.
... T. In short, we may represent the affine transformation S in the form TW. Using the fact that W and R commute the equation. R2T W + TWRnâ2 = TWR2 + Rnâ2.
Nov 11, 2011 - â Department of Mathematics, University of Aveiro, Campus de Santiago P-3810-193 Aveiro, Por- tugal ([email protected]). Supported by ...
are strongly multiplicative, all cycles, grids, wheels, and trees are. Theorem 3.1 ..... The first author wishes to thank the Mathematical Institute of Oxford. University ...
Feb 23, 2009 - A Shilla distance-regular graph Î (say with valency k) is a distance- ..... If Î is a Johnson graph, then c3 =9= a3 and it follows that Î = J(9, 3).
vertex. The face size is counted as the number of edge sides. (also called ..... triangular faces are merged into an octagon and the mesh genus is increased by 1.
Jun 20, 2016 - (ii) G acts strongly transitively on the spherical building at infinity ââ;. (iii) G acts cocompactly ..... the retraction of â onto A with center c. 5) The main examples ..... We call such an element g â StabG(A) a reflection-
Nov 19, 2016 - CO] 19 Nov 2016. Maximum matchings in regular .... Proof of Theorem 1.2. Since G is a simple graph, for each Qi, we have k|V (Qi)|â|[Qi,A]|. 2.
Jan 2, 2013 - BREAKER's bias b, we determine whether BREAKER wins (on any d-regular graph) or MAKER ..... The act of claiming one free edge by one of the players is called a step. ..... [6] Tibor Gallai, On directed graphs and circuits.
Definition 1.1 A k-regular graph on v vertices is a divisible design graph (DDG for .... if suffices to show that R has constant diagonal if and only if A3 has constant ...
... LAPACK library). You can find the Python versions of these on ..... to be the case, we scrap Aâ², and generate another random permutation, and thus another ...
May 10, 2016 - CT] 10 May 2016. AFFINE WEAKLY REGULAR TENSOR TRIANGULATED. CATEGORIES. IVO DELL'AMBROGIO AND DONALD STANLEY.
Construction of State Diagram of. Regular Expressions Using .... and b a. D P. D P P. D PQ. P D Q if. P. D PQ. D P Q otherwise. D f P Q f D P D Q ε ε δ δ ε. = = â . =.
Construction of strongly regular graphs using affine
W.D. Wallis. There is a ... equation (7) must be changed to. (7) k = n and the ... [7] W.D. Wallis, "Construction of strongly regular'graphs using affine designs", Bull.
BULL. AUSTRAL. MATH. SOC.
MOS 05B05, 05C99
VOL. 5 (1971), 431.
(O5B25, 62KI0)
Construction of strongly regular graphs using affine designs: Corrigenda W.D. Wallis There is a numerical error in the statement of Theorem 1 of [/].
The
expression (u-fc)u + (k-2)n which occurs in (6) must be replaced by (v-k)\i + (fc-2)nu , and a similar change must be made in line 5 of page !*6. As a consequence, equation (7) must be changed to (7)
k = n
and the definition of
x
to
x = (v-n)v in the statement of Theorem 2.
These changes are purely arithmetical, and
do not entail any further changes in the paper.
Reference [7]
W.D. Wallis, "Construction of strongly regular'graphs using affine designs", Bull. Austral. Math. Soc. 4 (1971), U1-U9.
University of Newcastle, Newcastle, New South Wales. Received 21 June 1971. The author is most grateful to Professor S.S. Shrikhande, who pointed out the error to him. 431
