Motivated by a longstanding conjecture of Thomassen, we study how large the average degree graph needs to be imply that it contains C4-free subgraph with at least t. Kühn and Osthus showed an bound which is double exponential in t sufficient. We give short proof this bound, before reducing single exponential. That is, show any G $$2^{ct^{2}\log\ t}$$ (for some constant c > 0) Finally, construct...

if $g$ is a connected graph with vertex set $v$, then the eccentric connectivity index of $g$, $xi^c(g)$, is defined as $sum_{vin v(g)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. in this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

We prove that for every k there exists d = d(k) such that every graph of average degree at least d contains a subgraph of average degree at least k and girth at least six. This settles a special case of a conjecture of Thomassen.

the paper presents a mathematical base modeling combined to modified-winding -function-approach (mwfa) for eccentricity fault detection of a round-rotor synchronous machine. for this aim, a 6-pole machine is considered, and the machine inductances are computed by mwfa in healthy and also under eccentricity fault. a numerical discrete-time method has been proposed to machine modeling in voltage-...

Temporal modulation sensitivity functions were measured centrally and at eccentricities of 2.5 degrees, 5 degrees and 10 degrees in the temporal visual field of 12 patients with recovered optic neuritis and in a group of matched normal controls. A circular, spatially uniform stimulus of 1 degree angular subtense was presented with sinusoidal modulation at 5, 8, 14 and 23 Hz. The general pattern...

The eccentricity distribution of exoplanets is known from radial velocity surveys to be divergent from circular orbits beyond 0.1 au. This is particularly the case for large planets where the radial velocity technique is most sensitive. The eccentricity of planetary orbits can have a large effect on the transit probability and subsequently the planet yield of transit surveys. The Kepler mission...

Abstract We introduce a broad class of multi-hooking networks, wherein multiple copies seed are hooked at each step random locations, and the number follows predetermined building sequence numbers. analyze degree profile in networks by tracking two kinds node degrees—the local average specific over time global overall graph. The former experiences phases latter is invariant with respect to type...