A vertex-transitive graph X is said to be half-arc-transitive if its automorphism group acts transitively on the set of edges of X but does not act transitively on the set of arcs of X. A classification of half-arc-transitive graphs on 4p vertices, where p is a prime, is given. Apart from an obvious infinite family of metacirculants, which exist for p=1(mod 4) and have been known before, there is an additional somewhat unique family of half-arc-transitive graphs of order 4p and valency 12; the latter exists only when p=1(mod 6) is of the form 2^{2k}+2^k+1, k ) 1.
COBISS.SI-ID: 4182632
A conjecture of Estrada and Rodrıguez-Velazquez [Phys. Rev. E 71, 056103 (2005)] that if a graph has identical subgraph centrality for all nodes, then the closeness and betweenness centralities are also identical for all nodes is disproved in this paper. It is observed that the counterexamples to the conjecture should be sought among walk-regular, non-vertex-transitive graphs and the search was performed by computer generation of graphs: among 63 883 116 regular graphs, there were 174 walk-regular graphs, out of which eight were non-vertex-transitive, which all represent counterexamples to the conjecture.
COBISS.SI-ID: 1024553556
In this paper, a particular shape preserving parametric polynomial approximation of conic sections is studied. The approach is based upon the parametric approximation of implicitly defined planar curves. Polynomial approximants derived are given in a closed form and provide the highest possible approximation order.
COBISS.SI-ID: 16716121
The existing classification of evolutionarily singular strategies in Adaptive Dynamics (Geritz et al. in Evol Ecol 12:35–57, 1998; Metz et al. in Stochastic and spatial structures of dynamical systems, pp 183–231, 1996) assumes an invasion fitness that is differentiable twice as a function of both the resident and the invading trait. Motivated by nested models for studying the evolution of infectious diseases (Boldin, Diekmann: Journal of Mathematical Biology, Volume 56 (2008), Issue 5, pp. 635-672.), we consider an extended framework in which the selection gradient exists (so the definition of evolutionary singularities extends verbatim), but where the invasion fitness may lack the smoothness necessary for the classification à la Geritz et al. We derive the classification of singular strategies with respect to convergence stability and invadability and determine the condition for the existence of nearby dimorphisms. In addition to ESSs and invadable strategies, we observe what we call one-sided ESSs: singular strategies that are invadable from one side of the singularity but uninvadable from the other. Studying the regions of mutual invadability in the vicinity of a one-sided ESS, we discover that two isoclines spring in a tangent manner from the singular point at the diagonal of the mutual invadability plot. The way in which the isoclines unfold determines whether these one-sided ESSs act as ESSs or as branching points. We present a computable condition that allows one to determine the relative position of the isoclines (and thus dimorphic dynamics) from the dimorphic as well as from the monomorphic invasion exponent and illustrate our findings with an example from evolutionary epidemiology.
COBISS.SI-ID: 1024534868
A w-container C(u,v) of a graph G is a set of w-disjoint paths joining u to v. A w-container of G is a w*-container if it contains all the nodes of V(G). A bipartite graph G is w*-laceable if there exists a w*-container between any two nodes from different parts of G. Let n and k be any two positive integers with n ) 1 and k ( n+1. In this paper, we prove that n-dimensional bipartite hypercube-like graphs are f-edge fault k∗-laceable for every f ( n-1 and f+k ( n+1.
COBISS.SI-ID: 1024516436