On the minimum rank of not necessarily symmetric matrices: a preliminary study.
On the minimum vector rank of multigraphs.
On the minus domination number of graphs
Let be a simple graph. A -valued function is said to be a minus dominating function if for every vertex , , where is the closed neighborhood of . The weight of a minus dominating function on is . The minus domination number of a graph , denoted by , equals the minimum weight of a minus dominating function on . In this paper, the following two results are obtained. (1) If is a bipartite graph of order , then (2) For any negative integer and any positive integer , there exists...
On the modes of polynomials derived from nondecreasing sequences.
On the monochromatic Schur triples type problem.
On the monotone upper bound problem.
On the most weight vectors in a dimension binary code.
On the multiplicative independence of binomial coefficients
On the multiplicity of Laplacian eigenvalues for unicyclic graphs
Let be a connected graph of order and a unicyclic graph with the same order. We firstly give a sharp bound for , the multiplicity of a Laplacian eigenvalue of . As a straightforward result, . We then provide two graph operations (i.e., grafting and shifting) on graph for which the value of is nondecreasing. As applications, we get the distribution of for unicyclic graphs on vertices. Moreover, for the two largest possible values of , the corresponding graphs are completely...
On the multiplicity of Laplacian eigenvalues of graphs
In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered.
On the -conjecture
On the -modules generated by partitions of a given shape.
On the Nilpotent representations of GLn (O).
On the noncommuting graph associated with a finite group.
On the Non-Existence of Certain M.D.S. Codes and Projective Planes.
On the Non-Existence of Certain Nearly Regular Planar Maps with Two Exceptional Faces
On the non-holonomic character of logarithms, powers, and the th prime function.
On the Non-(p−1)-Partite Kp-Free Graphs
We say that a graph G is maximal Kp-free if G does not contain Kp but if we add any new edge e ∈ E(G) to G, then the graph G + e contains Kp. We study the minimum and maximum size of non-(p − 1)-partite maximal Kp-free graphs with n vertices. We also answer the interpolation question: for which values of n and m are there any n-vertex maximal Kp-free graphs of size m?
On the normal disconnection of a tree
On the norms of the random walks on planar graphs
We consider the nearest neighbor random walk on planar graphs. For certain families of these graphs, we give explicit upper bounds on the norm of the random walk operator in terms of the minimal number of edges at each vertex. We show that for a wide range of planar graphs the spectral radius of the random walk is less than one.