Let g(2n, l, d) be the number of general cubic graphs on 2n labeled vertices with l loops and d double edges. We use inclusion and exclusion with two types of properties to determine the asymptotic behavior of g(2n, l, d) and hence that of g(2n), the total number of general cubic graphs of order 2n. We show that almost all general cubic graphs are connected. Moreover, we determined the asymptot...

Many woody eudicot plants form a secondary xylem composed of gelatinous fibers (G-fibers) called "tension wood" (TW) along the upper side tilted stem or branch. TW generates large tensile growth stress in longitudinal direction, allowing branch to develop negative-gravitropism response strong gravitational stimulus. This is because G-fiber tends contract direction as it matures. The matured als...

By a graph, we mean a finite undirected simple graph with no loops and no multiple edges. For a graph G and an edge e of G, we let G/e denote the graph obtained from G by contracting e (and replacing each pair of the resulting double edges by a simple edge). Let k ≥ 2 be an integer, and let G be a k-connected graph. An edge e of G is said to be k-contractible if G/e is k-connected. The set of k...

Consider a set of simple closed curves on a surface of genus g which fill the surface and which pairwise intersect at most once. We show that the asymptotic growth rate of the smallest number in such a set is 2 √ g as g → ∞. More generally, we give a precise asymptotic for filling sets of curves which pairwise intersect at most K ≥ 1 times. We then bound from below the cardinality of a filling ...

We examine homozygosity and G(st) for a subdivided population governed by the finite island model. Assuming an infinite allele model and strong mutation we show that the steady state distributions of G(st) and homozygosity have asymptotic expansions in the mutation rate. We use this observation to derive asymptotic expansions for various moments of homozygosity and to derive rigorous formulas f...

The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is study asymptotic performance posterior distribution frequentist setting. present paper contributes area by formulating a contraction for linear problems, truncated Gaussian series priors, and under general smoothness assumptio...

In this paper, we present the concept of conventional $F_G$-contraction and prove results a new coincidence point for multi-valued in b-metric spaces endowed with digraph $G.$

If G is a graph, and if for e = uv ? E(G) the number of vertices closer to u than v denoted by nu, then Mo(G) uv?E(G) |nu-nv| Mostar index G. In this paper, studied on trees graph products. Lower upper bounds are given difference between indices tree obtained contraction one its edges corresponding extremal characterized. An bound class all but stars proved. Extremal also determined (k+1)-th la...

In great generality, the basic steady-state distributions in the BMAP / G /1 queue have asymptotically exponential tails. Here we develop asymptotic expansions for the asymptotic decay rates of these tail probabilities in powers of one minus the traffic intensity. The first term coincides with the decay rate of the exponential distribution arising in the standard heavy-traffic limit. The coeffi...