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Circuit and cocircuit partitions of binary matroids

Eunice Gogo Mphako (2006)

Czechoslovak Mathematical Journal

We give an example of a class of binary matroids with a cocircuit partition and we give some characteristics of a set of cocircuits of such binary matroids which forms a partition of the ground set.

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Baicheva, Tsonka, Topalova, Svetlana (2015)

Serdica Journal of Computing

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant...

Closure conditions of commutativity

Václav J. Havel, Josef Klouda (1994)

Archivum Mathematicum

There are investigated some closure conditions of Thomsen type in 3-webs which gurantee that at least one of coordinatizing quasigroups of a given 3-web is commutative.

Coalescing Fiedler and core vertices

Didar A. Ali, John Baptist Gauci, Irene Sciriha, Khidir R. Sharaf (2016)

Czechoslovak Mathematical Journal

The nullity of a graph G is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex of unique...

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