An oriented colouring of planar graphs with girth at least 4.
An Oriented Version of the 1-2-3 Conjecture
The well-known 1-2-3 Conjecture addressed by Karoński, Luczak and Thomason asks whether the edges of every undirected graph G with no isolated edge can be assigned weights from {1, 2, 3} so that the sum of incident weights at each vertex yields a proper vertex-colouring of G. In this work, we consider a similar problem for oriented graphs. We show that the arcs of every oriented graph −G⃗ can be assigned weights from {1, 2, 3} so that every two adjacent vertices of −G⃗ receive distinct sums of outgoing...
An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits.
An umbral calculus for polynomials characterizing tensor products.
An upper bound for domination number of 5-regular graphs
Let be a simple graph. A subset is a dominating set of , if for any vertex , there exists a vertex such that . The domination number, denoted by , is the minimum cardinality of a dominating set. In this paper we will prove that if is a 5-regular graph, then .
An upper bound for graphs of diameter 3 and given degree obtained as abelian lifts of dipoles
We derive an upper bound on the number of vertices in graphs of diameter 3 and given degree arising from Abelian lifts of dipoles with loops and multiple edges.
An upper bound for maximum number of edges in a strongly multiplicative graph
In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bounds given by Beineke and Hegde [3] and Adiga, Ramaswamy and Somashekara [2], for n ≥ 28.
An upper bound for the minimum degree of a graph
An upper bound for the minimum valency of a graph embedded in a compact 2-manifold
An upper bound for the representation number of graphs with fixed order.
An upper bound for the shortest hamiltonian path in the symmetric euclidean case
An upper bound of a generalized upper Hamiltonian number of a graph
In this article we study graphs with ordering of vertices, we define a generalization called a pseudoordering, and for a graph we define the -Hamiltonian number of a graph . We will show that this concept is a generalization of both the Hamiltonian number and the traceable number. We will prove equivalent characteristics of an isomorphism of graphs and using -Hamiltonian number of . Furthermore, we will show that for a fixed number of vertices, each path has a maximal upper -Hamiltonian...
An upper bound of the basis number of the strong product of graphs
The basis number of a graph G is defined to be the least integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. In this paper we give an upper bound of the basis number of the strong product of a graph with a bipartite graph and we show that this upper bound is the best possible.
An upper bound on algebraic connectivity of graphs with many cutpoints.
An upper bound on the basis number of the powers of the complete graphs
The basis number of a graph is defined by Schmeichel to be the least integer such that has an -fold basis for its cycle space. MacLane showed that a graph is planar if and only if its basis number is . Schmeichel proved that the basis number of the complete graph is at most . We generalize the result of Schmeichel by showing that the basis number of the -th power of is at most .
An upper bound on the domination number of a graph.
An upper bound on the Laplacian spectral radius of the signed graphs
In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.
An upper estimate of the number of edges of a hypergraph with given diameter
Analoga of Menger's theorem for polar and polarized graphs
Analogies entre espaces hyperboliques réels et l’arbre de Bruhat-Tits sur