A note on the largest eigenvalue of non-regular graphs.
A note on the modified -Bernstein polynomials.
A note on the non-colorability threshold of a random graph.
A note on the number of associative triples in finite commutative Moufang loops
A note on the number of derangements.
A note on the number of edges guaranteeing a in Eulerian bipartite digraphs.
A note on the number of Hamiltonian paths in strong tournaments.
A note on the number of squares in a partial word with one hole
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence starts. In this paper, we investigate squares in partial words with one hole, or sequences over a finite alphabet that have a “do not know” symbol or “hole”. A square in a partial word over a given alphabet has the form uv where u is compatible with v, and consequently, such square is...
A note on the open packing number in graphs
A subset of vertices in a graph is an open packing set if no pair of vertices of has a common neighbor in . An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The maximum cardinality of an open packing set is called the open packing number and is denoted by . A subset in a graph with no isolated vertex is called a total dominating set if any vertex of is adjacent to some vertex of . The total domination number of , denoted...
A Note on the p−Center Problem
A Note on the Permanental Roots of Bipartite Graphs
It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing...
A Note on the Powers of 2-Connected Graphs.
A note on the problem of finding a (3,9)-cage.
A note on the -binomial rational root theorem.
A note on the -Genocchi numbers and polynomials.
A note on the radius of iterated line graphs.
A note on the Ramsey number and the planar Ramsey number for C₄ and complete graphs
We give a lower bound for the Ramsey number and the planar Ramsey number for C₄ and complete graphs. We prove that the Ramsey number for C₄ and K₇ is 21 or 22. Moreover we prove that the planar Ramsey number for C₄ and K₆ is equal to 17.
A note on the Ramsey-type theorem of Erdös
A note on the rank of self-dual polyhedra
A note on the realizaiton of distances within sets in euclidean space.