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Exact Bounds on the order of the maximum clique of a graph
, 2003
"... The paper reviews some of the existing exact bounds to the maximum clique of a graph and successivel presents a new upper and a newlwx, bound. The new upper bound is rank # A=2, where # A is the adjacency matrix of the compljWxyjkV graph, and derives from a formuly,G8 of the maximumclimu ..."
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The paper reviews some of the existing exact bounds to the maximum clique of a graph and successivel presents a new upper and a newlwx, bound. The new upper bound is rank # A=2, where # A is the adjacency matrix of the compljWxyjkV graph, and derives from a formuly,G8 of the maximumclimu problm incompl9 space. The newlwxj bound is ! 1=(1 g j # (# # )) (see text fordetail8 and improves strictl the present best lstx bound publdxWW byWil (J. Combin. Theory Ser. B 40 (1986) 113). Throughout
Computers and Discovery in Algebraic Graph Theory
 Edinburgh, 2001), Linear Algebra Appl
, 2001
"... We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. ..."
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We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.
unknown title
, 2002
"... www.elsevier.com/locate/laa On completely positive graphs and their complements ..."
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www.elsevier.com/locate/laa On completely positive graphs and their complements
Laplacians of Graphs, QuasiStrongly Regular Graphs and Completely Positive Graphs
"... I am deeply grateful to my advisor, Professor Abraham Berman, for his constant support and kind help in all my endeavours. I thank my friends Yulia Bougaev, Natan Keller, Dr. Uri Onn and Gregory Shapiro for valuable remarks and enlightening discussions. I thank my wonderful family and especially my ..."
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I am deeply grateful to my advisor, Professor Abraham Berman, for his constant support and kind help in all my endeavours. I thank my friends Yulia Bougaev, Natan Keller, Dr. Uri Onn and Gregory Shapiro for valuable remarks and enlightening discussions. I thank my wonderful family and especially my little sister Patricia for making this undertaking possible. The generous financial help of the Chais Family Foundation
(G) 1
, 2003
"... Let (G) be the largest eigenvalue of the adjacency matrix of a graph G: We show that if G is Kp+1free then ..."
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Let (G) be the largest eigenvalue of the adjacency matrix of a graph G: We show that if G is Kp+1free then
A Tool for Optimal Weak Sense of Direction
, 2000
"... Weak sense of direction is a property of the labelling of (possibly anonymous) networks that allows one to assign coherently local identifiers to other processors on the basis of the route followed by incoming messages. Though there exists a linear algorithm that allows one to assign a weak sense of ..."
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Weak sense of direction is a property of the labelling of (possibly anonymous) networks that allows one to assign coherently local identifiers to other processors on the basis of the route followed by incoming messages. Though there exists a linear algorithm that allows one to assign a weak sense of direction to any given network, the number of colours used in such construction may be as large as the number of processors. It is an open, difficult, yet intriguing problem that of establishing an optimal weak sense of direction for a given graph, that is, a weak sense of direction using as few colours as possible. To attack this problem, we have developed an implicit enumeration algorithm that searches for optimal weak sense of direction; the algorithm is implemented in a publicly available tool, optwsod. Although optwsod can only deal with graphs that are reasonably small, we think that the results obtained (some examples are presented at the end of the paper) are sometimes surprising an...