An inequality related to Vizing's conjecture.
An infinite family of graphs with the same Ihara Zeta function.
An introduction to -graphs, a graph-theoretic representation of natural numbers.
An invariant for finitely presented ...G-modules.
An Inversion Formula for the Radon Transform on Trees.
An inversion formula, matrix functions, combinatorial identities and graphs
An optimal matching problem
Given two measured spaces and , and a third space , given two functions and , we study the problem of finding two maps and such that the images and coincide, and the integral is maximal. We give condition on and for which there is a unique solution.
An optimal matching problem
Given two measured spaces and , and a third space Z, given two functions u(x,z) and v(x,z), we study the problem of finding two maps and such that the images and coincide, and the integral is maximal. We give condition on u and v for which there is a unique solution.
An optimal strongly identifying code in the infinite triangular grid.
An ordering of some metrics defined on the space of graphs
An oriented 7-colouring of planar graphs with girth at least 7.
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 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