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- Aleksandar Jurisic, Jacobus H. Koolen
- Discrete Mathematics
- 2002

Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves also figured prominently in the recent proof of Fermat's… (More)

We consider a distance-regular graph ? with diameter d 3 and eigenvalues k = 0 > 1 > > d. We show the intersection numbers a 1 ; b 1 satisfy (a 1 + 1) 2 : We say ? is tight whenever ? is not bipartite, and equality holds above. We characterize the tight property in a number of ways. For example, we show ? is tight if and only if the intersection numbers are… (More)

- Aleksandar Jurisic, Jacobus H. Koolen
- Eur. J. Comb.
- 2000

- Aleksandar Jurisic, Jacobus H. Koolen
- Des. Codes Cryptography
- 2000

Let ? be a distance-regular graph with diameter d. For vertices x and y of ? at distance i, 1 i d, we deene the sets (x) \ ?(y). Then we say ? has the CAB j property, if the partition CAB i (x; y) = fC i (x; y); A i (x; y); B i (x; y)g of the local graph of y is equitable for each pair of vertices x and y of ? at distance i j. We show that if ? has the CAB… (More)

- Aleksandar Jurisic
- Discrete Mathematics
- 1998

Antipodal covers of strongly regular graphs which are not necessarily distance-regular are studied. The structure of short cycles in an antipodal cover is considered. In most cases, this provides a tool to determine if a strongly regular graph has an antipodal cover. In these cases, covers cannot be distance-regular except when they cover a complete… (More)

- Aleksandar Jurisic, Jacobus H. Koolen, Arjana Zitnik
- Eur. J. Comb.
- 2008

In this paper, triangle-free distance-regular graphs with diameter 3 and an eigenvalue θ with multiplicity equal to their valency are studied. Let Γ be such a graph. We first show that θ = −1 if and only if Γ is antipodal. Then we assume that the graph Γ is primitive. We show that it is formally self-dual (and hence Q-polynomial and 1-homogeneous), all its… (More)

- Kris Coolsaet, Aleksandar Jurisic, Jacobus H. Koolen
- Eur. J. Comb.
- 2008

Let Γ be a triangle-free distance-regular graph with diameter d ≥ 3, valency k ≥ 3 and intersection number a 2 = 0. Assume Γ has an eigenvalue with multiplicity k. We show that Γ is 1-homogeneous in the sense of Nomura when d = 3 or when d ≥ 4 and a 4 = 0. In the latter case we prove that Γ is an antipodal cover of a strongly regular graph, which means that… (More)

- Aleksandar Jurisic, Jacobus H. Koolen, Stefko Miklavic
- J. Comb. Theory, Ser. B
- 2005

We classify triangle-and pentagon-free distance-regular graphs with diameter d ≥ 2, valency k, and an eigenvalue multiplicity k. In particular, we prove that such a graph is isomorphic to a cycle, a k-cube, a complete bipartite graph minus a matching, folded k-cube, k odd and k ≥ 7. This is a generalization of the results of Nomura [10] and Yamazaki [13],… (More)

- Aleksandar Jurisic, Paul Terwilliger, Arjana Zitnik
- Eur. J. Comb.
- 2010