Some Characterizations of Nilpotent Lie Algebras.
On a conjecture of the semigroup of fully indecomposable relations
On the classification and toughness of generalized permutation star-graphs
We use an algebraic method to classify the generalized permutation star-graphs, and we use the classification to determine the toughness of all generalized permutation star-graphs.
An application of Pólya’s enumeration theorem to partitions of subsets of positive integers
Let be a non-empty subset of positive integers. A partition of a positive integer into is a finite nondecreasing sequence of positive integers in with repetitions allowed such that . Here we apply Pólya’s enumeration theorem to find the number of partitions of into , and the number of distinct partitions of into . We also present recursive formulas for computing and .
On the toughness of cycle permutation graphs
Motivated by the conjectures in [11], we introduce the maximal chains of a cycle permutation graph, and we use the properties of maximal chains to establish the upper bounds for the toughness of cycle permutation graphs. Our results confirm two conjectures in [11].
A generalization of a theorem of Boolean relation matrices
On the semigroup of fully indecomposable relations
Uniquely -colorable and chromatically equivalent graphs.
A remark on the eigenvalues of generalized circulants
Some applications of a theorem of Schur to graphs and to a class of endomorphisms
A note on regular automorphisms of algebras
Equivalence classes of functions on finite sets.
Some families of -graphs.
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