In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.

A space X is called an α-Toronto space if X is scattered of Cantor– Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each

For a graph G let μ(G) denote the cyclomatic number and let ν(G) denote the maximum number of edge-disjoint cycles of G. We prove that for every k ≥ 0 there is a finite set P(k) such that every 2-connected graph G for which μ(G)− ν(G) = k arises by applying a simple extension rule to a graph in P(k). Furthermore, we determine P(k) for k ≤ 2 exactly.

January 15, 2017 Version 3.0.0 Date 2016-09-16 Title Rank Product method for identifying differentially expressed genes with application in meta-analysis Author Francesco Del Carratore , Andris Janckevics Fangxin Hong , Ben Wittner , Rainer Breitling <r.breitling...

March 29, 2017 Version 3.0.0 Date 2016-09-16 Title Rank Product method for identifying differentially expressed genes with application in meta-analysis Author Francesco Del Carratore , Andris Janckevics Fangxin Hong , Ben Wittner , Rainer Breitling <r.breitling@b...

Let the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that, for every integer c ≥ 2, there are at most finitely many trunks of semiharmonic graphs with cyclomatic number c — in contrast to the fact established by the last two of the present authors in their paper Semiharmonic Bicyclic Graphs (this journal) that there are infinitely many connected semiharmonic gr...

in this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated