On the maximum average degree and the incidence chromatic number of a graph.
On the Maximum Eigenvalue of a Reducible Non-Negative Real Matrix.
On the Maximum Genus of Some Graphs With Upper Imbeddable Subgraphs..
On the maximum number of arcs in some classes of graphs
On the Maximum of a Branching Process Conditioned on the Total Progeny
The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.
On the maximum positive semi-definite nullity and the cycle matroid of graphs.
On the minimal basis of the spindle-surface .
On the minimal length of the longest trail in a fixed edge-density graph
A nearly sharp lower bound on the length of the longest trail in a graph on n vertices and average degree k is given provided the graph is dense enough (k ≥ 12.5).
On the minimum degree and edge-connectivity of a graph
On the minimum number of components in a cotree of a graph
On the minimum number of vertices and edges in a graph with a given number of spanning trees
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 monotone upper bound problem.
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 noncommuting graph associated with a finite group.
On the Non-Existence of Certain Nearly Regular Planar Maps with Two Exceptional Faces
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?