The maximal spectral radius of a digraph with edges.
The maximum clique and the signless Laplacian eigenvalues
Lower and upper bounds are obtained for the clique number and the independence number , in terms of the eigenvalues of the signless Laplacian matrix of a graph .
The maximum genus, matchings and the cycle space of a graph
In this paper we determine the maximum genus of a graph by using the matching number of the intersection graph of a basis of its cycle space. Our result is a common generalization of a theorem of Glukhov and a theorem of Nebeský .
The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree
The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2. Using a combinatorial...
The maximum number of edges in a three-dimensional grid-drawing.
The maximum number of perfect matchings in graphs with a given degree sequence.
The maximum of the maximum rectilinear crossing numbers of -regular graphs of order .
The maximum order of finite groups of outer automorphisms of free groups.
The maximum path theorem and extreme points of James space
The Median Problem on k-Partite Graphs
In a connected graph G, the status of a vertex is the sum of the distances of that vertex to each of the other vertices in G. The subgraph induced by the vertices of minimum (maximum) status in G is called the median (anti-median) of G. The median problem of graphs is closely related to the optimization problems involving the placement of network servers, the core of the entire networks. Bipartite graphs play a significant role in designing very large interconnection networks. In this paper, we...
The Merris index of a graph.
The middle graph of a hypergraph
The minimum number of monotone subsequences.
The minimum rank problem over finite fields.
The minimum spectral radius of graphs with a given clique number.
The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number
In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.
The min-max supergraph
The minor crossing number of graphs with an excluded minor.
The modified negative decision number in graphs.
The monadic second-order logic of graphs III : tree-decompositions, minors and complexity issues