Let G1 and G2 be copies of a graph G, and let f : V (G1) → V (G2) be a function. Then a functigraph C(G, f) = (V, E) is a generalization of a permutation graph, where V = V (G1) ∪ V (G2) and E = E(G1) ∪ E(G2) ∪ {uv : u ∈ V (G1), v ∈ V (G2), v = f(u)}. In this paper, we study colorability and planarity of functigraphs.
everal myxosporean parasites are of importance in fisheries and aquaculture in British Columbia. The PKX organism and Ceratomyxa shasta Noble, 1950 cause disease and mortality, Kudoa thyrsiles (Gilchrist, 1924) and Henneguya salminicola Ward, 1919 are of importance because they infect somatic muscle, cause unsightly cysts and soft flesh, and thus reduce the market value of the fish. Myxobolus arcticus Pugachev et Khokhlov, 1979, an apparently non-pathogenic species, along with H. salminicola, is used as a biological tag in fishery management. Myxobolus arcticus has also been used in our laboratory as a model for the study of myxosporean life cycles. Other myxosporeans that have been found in salmonids in British Columbia include Myxobolus squamalis (Iverson, 1954), Myxobolus insidiosus Wyatt et Pratt, 1963, Myxidium truitae Léger, 1930, Myxidium salvelini Shuhnan et Konovalov, 1966, Chloromyxum sp., ľarvicapsula sp., and Sphaerospora sp.
The elements of economic interest in coastal sediments are characterized by a relative high concentration in minerals as the ilmenite, rutile, monazite and manganite. The objective of this work has been to carry out a study of selective sequential extractions of lanthanide elements and metals that are toxic. It started with rare earth phosphate minerals, using the technology established in the American continent (Tessier), applicable to sludge and sediments. The study is concerned with the outcrops of REE's minerals reported in Mexico as pegmatite, in the settlement "The Dead”, Telixtlahuaca, Oaxaca and of “Lagoon Mother” and “Saw of San Carlos”, Tamaulipas. There were evaluated in addition samples of Cuarzomonzodiorite, of “The Incarnation”, Hidalgo. Two modifications interfere to the above mentioned scheme of extractions and for the reached results it was possible to find the existence of some elements lanthanides as well as of toxic metals, praseodymium, neodymium, ytterbium and lead, associated with these minerals. The procedure of sequential selective extractions according to Tessier's methodology, does not manage to extract significant quantities of these elements, except in the conditions of maximum aggressiveness, of a digestion with HNO3/HClO4 concentrates and warming.