Distance-regular graph with the intersection array {45, 30, 7; 1, 2, 27} does not exist
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A. L. Gavrilyuk
Abstract
A distance-regular graph is called geometric if each its edge belongs to a unique maximal clique on the size of which the Hoffman-Delsarte inequality is satisfied as equality. A geometric classification of distance-regular graphs containing no 4-claws was put forward by S. Bang. In the present paper we refine the description of one class of such graphs. In particular, it is shown that a graph with the intersection array {45, 30, 7; 1, 2, 27} does not exist.
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 12-01-00012), the Department of Mathematical Sciences of RAS (grant no. 12-T-1-1003), the Joint Research Program of the Ural and Siberian Branches of RAS (grant no. 12-C-1-1018), the International Joint Research Fund between NSFC (China) and RFBR (grant no. 12-01-91155). The first author was supported by the Council of the President of the Russian Federation for the Support of Young Scientists (grant no. MK- 938.2011.1).
© 2014 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Distance-regular graph with the intersection array {45, 30, 7; 1, 2, 27} does not exist
- The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem
- Traveling salesman polytopes and cut polytopes. Affine reducibility
- Minors of the constraint matrix in multi-index transport problems
- Cycle structure of power mappings in a residue classes ring
- A criterion for the automata realizable functions to be boundedly deterministic
- On the complexity of two-dimensional discrete logarithm problem in a finite cyclic group with effective automorphism of order
- The completeness criterion for some systems containing P-sets of automaton functions
- On the synthesis of circuits admitting complete fault detection test sets of constant length under arbitrary constant faults at the outputs of the gates
- Factorially solvable rings
- Identities with permutations and quasigroups isotopic to groups and to Abelian groups
- Classes of projectively equivalent quadrics over local rings
