For every r ∈ N, let θr denote the graph with two vertices and r parallel edges. The θr-girth of a graph G is the minimum number of edges of a subgraph of G that can be contracted to θr. This notion generalizes the usual concept of girth which corresponds to the case r = 2. In [Minors in graphs of large girth, Random Structures & Algorithms, 22(2):213–225, 2003], Kühn and Osthus showed that gra...

Large-girth quasi-cyclic LDPC codes have been experimentally evaluated for use in PMD compensation by turbo equalization for a 10 Gb/s NRZ optical transmission system, and observing one sample per bit. Net effective coding gain improvement for girth-10, rate 0.906 code of length 11936 over maximum a posteriori probability (MAP) detector for differential group delay of 125 ps is 6.25 dB at BER o...

Objective: To determine the relationship between asymmetries in lower leg girth and standing heel-rise after anterior cruciate ligament (ACL) reconstruction. Design: Single-group posttest. Participants: 15 at a mean of 30 d after ACL reconstruction. Measurements: Lower leg girth and number of repetitions performed on the standing heel-rise test. Results: A significant decrease in lower leg girt...

A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. We show that a symmetric cubic graph of girth at most 9 is either 1-regular or 2-regular (following the notation of Djokovic), or...

The girth is the length of shortest cycle in a graph. Recently, the problem for computing the girth of a graph have been studied well. Itai and Rodeh developed the first non trivial algorithm for computing girth in general graphs. Their algorithm runs in O (nm) time in the worst case and it runs in O(n) time on average case. For unweighted planer graphs, Djidjev gave a O ( n log n ) time algori...

This study was carried out to examine the effect of selected fruit peels on growth and yield okra (Abelmoschus esculentus). 10g ground banana, watermelon, pawpaw, pineapple, plantain, orange applied 7 kg soil left for days before planting seed. NPK (15:15:15) serves as positive control while groups without fertilizer served negative study. Each treatment replicated five times in polythene bags ...

An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if a path of length two exists between them. In this paper some results on injective colorings of planar graphs with few colors are presented. We show that all planar graphs of girth ≥19 and maximum degree ∆ are injectively ∆-colorable. We also show that all planar graphs of girth ≥10 are injectively (...