It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.

In this writing, we point out some errors made in Boutin (Graphs Combin 25:789–806, 2009), where the author claims that a maximal independent set hereditary system is minimal determining (resolving) set. Further more, if exchange property holds at level of resolving sets, then, corresponding matroid. We give counter examples to disprove both her claims. Besides, prove there exist graphs having ...

We prove that an associative algebra A is isomorphic to a subalgebra of a C∗-algebra if and only if its ∗-double A∗A∗ is ∗-isomorphic to a ∗-subalgebra of a C∗-algebra. In particular each operator algebra is shown to be completely boundedly isomorphic to an operator algebra B with the greatest C∗-subalgebra consisting of the multiples of the unit and such that each element in B is determined by...

Reports of key MIS issues based on the perceptions of senior IS executives appear periodically in the MIS literature. In this article, we provide another perspective on key MIS issues by examining published MIS articles. A content analysis of MIS articles appearing between 1989 and mid-year 1993 in prominent academic and practitioner journals has been conducted in order to: identify, classify, ...

Let G = (S,E) be a plane straight line graph on a finite point set S ⊂ R in general position. For a point p ∈ S let the maximum incident angle of p in G be the maximum angle between any two edges of G that appear consecutively in the circular order of the edges incident to p. A plane straight line graph is called φopen if each vertex has an incident angle of size at least φ. In this paper we st...

For the assignment game, we propose the following selling mechanism: sellers, simultaneously, fix their prices first; then buyers, sequentially, decide which object to buy, if any. The first phase of the game determines the potential prices, while the second phase determines the actual matching. We prove that the set of subgame perfect equilibria in pure strategies in the strong sense of the me...

Several authors have investigated conditions for a binary block design, D, to be maximally robust such that every eventual design obtained from D by eliminating r[υ] − 1 blocks, is connected, where r[υ] is the smallest treatment replication. Four new results for the maximal robustness of D with superior properties are given. An extension of these results to widen the assessment of robustness of...

Over the past decade, the relationship between IT and performance has been one of the most actively researched topics in MIS. Since Robert Solow quipped that “You can see the computer age everywhere but in the productivity statistics,” over 50 empirical studies have investigated IT’s impacts on productivity and performance. These studies have been motivated by the economic paradox implicit in S...

Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. We consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem...