Finite planar vertex-transitive graphs of the regularity degree three
Finite simple groups of Lie type as expanders
We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This confirms a conjecture of Babai, Kantor and Lubotzky from 1989, which has already been proved by Kassabov for sufficiently large rank. The bounded rank case is deduced here from a uniform result for which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.
Finite spherical geometries
Finite Vertex-Transitive Planar Graphs of the Regularity Degree Four or Five
Finite-size scaling in percolation.
Finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures
In this paper, we investigate the finite-time adaptive outer synchronization between two complex dynamical networks with nonidentical topological structures. We propose new adaptive controllers, with which we can synchronize two complex dynamical networks within finite time. Sufficient conditions for the finite-time adaptive outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to demonstrate the effectiveness and feasibility of the...
Fixed point results on a metric space endowed with a finite number of graphs and applications
In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.
Fixed point theorems in CAT(0) spaces and -trees.
Fixed points of two-sided fractional matrix transformations.
Fixed simplex property for retractable complexes.
Fixed-point-free embeddings of graphs in their complements.
Fixing numbers of graphs and groups.
Fixpunkteigenschaften von automorphismen spezieller, endlicher, ebener, dreifach-knotenzusammenhängender graphen
Flexibility of embeddings of bouquets of circles on the projective plane and Klein bottle.
Flexible color lists in Alon and Tarsi's theorem, and time scheduling with unreliable participants.
Flows on the join of two graphs
The join of two graphs and is a graph formed from disjoint copies of and by connecting each vertex of to each vertex of . We determine the flow number of the resulting graph. More precisely, we prove that the join of two graphs admits a nowhere-zero -flow except for a few classes of graphs: a single vertex joined with a graph containing an isolated vertex or an odd circuit tree component, a single edge joined with a graph containing only isolated edges, a single edge plus an isolated...
Folding on the wedge sum of graphs and their fundamental group.
Food Webs, Competition Graphs, and Habitat Formation
One interesting example of a discrete mathematical model used in biology is a food web. The first biology courses in high school and in college present the fundamental nature of a food web, one that is understandable by students at all levels. But food webs as part of a larger system are often not addressed. This paper presents materials that can be used in undergraduate classes in biology (and mathematics) and provides students with the opportunity...
For which graphs does every edge belong to exactly two chordless cycles?
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced...