We describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least k ≥ 5 which are very efficient for 5 ≤ k ≤ 7 and show how these algorithms can be efficiently restricted to generate snarks with girth at least k. Our implementation of these algorithms is more than 30, respectively 40 times faster than the previously fastest generator for cubic graphs with ...

We show that every n-vertex cubic graph with girth at least g have domination number at most 0.299871n + O (n/g) < 3n/10 + O (n/g).

A run is an inclusion maximal occurrence in a string (as a subinterval) of a factor in which the period repeats at least twice. The maximal number of runs in a string of length n has been thoroughly studied, and is known to be between 0.944n and 1.029n. The proofs are very technical. In this paper we investigate cubic runs, in which the period repeats at least three times. We show the upper bou...

One of the problems encountered by engineering students and faculty staff members Aurora State College Technology (ASCOT) is water supply for toilet urinal flushing. This problem attributed to location area which 50m above sea level. The main source campus coming from falls requires pipelines that are vulnerable heavy damage during natural disasters illegal intrusion. To address scarcity, rainw...

The patterned template-assisted assembly of the cubic microparticles driven by the competing capillary, Columbic, and van der Waals forces had been studied in comparison with the traditional spherical colloidal microparticles. We observed that the spherical and cubic microparticles assembled with different probability in the channels of the hydrophobic-hydrophilic patterned substrates due to di...

We introduce weak oddness ωw, a new measure of uncolourability of cubic graphs, defined as the least number of odd components in an even factor. For every bridgeless cubic graph G, %(G) ≤ ωw(G) ≤ ω(G), where %(G) denotes the resistance of G and ω(G) denotes the oddness of G, so this new measure is an approximation of both oddness and resistance. We demonstrate that there are graphs G satisfying...

A coastal community vulnerability index (CCVI) was constructed to evaluate the vulnerability of coastal communities (Buhangin, Pingit, Reserva, Sabang, and Zabali) in the municipality of Baler, Aurora, Philippines. This index was composed of weighted averages of seven vulnerability factors namely geographical, economic and livelihood, food security, environmental, policy and institutional, demo...