Ela the M-competition Indices of Symmetric Primitive Digraphs without Loops

The m-competition indices of symmetric primitive digraphs with loop

Well primitive digraphs

A primitive digraph D is said to be well primitive if the local exponents of D are all equal. In this paper we consider well primitive digraphs of two special types: digraphs that contain loops, and symmetric digraphs with shortest odd cycle of length r. We show that the upper bound of the exponent of the well primitive digraph is n− 1 in both these classes of digraphs, and we characterize the ...

A Characterization of Graphs with Interval Two-Step Graphs

Dedicated by the other authors to Professor John Maybee on the occasion of his 65th birthday. Abstract. One of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. This problem originated in the work of Cohen 5, 6] on food webs. In this paper we consider this problem for the class of loopless symmetric digraphs. The competition graph ...

Flag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups

The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).

Constructing continuum many countable, primitive, unbalanced digraphs

We construct continuum many non-isomorphic countable digraphs which are highly arc-transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive. 2000 Mathematics Subject Classification: 20B07, 20B15, 03C50, 05C20.