Critical Pebbling Numbers of Graphs

We define three new pebbling parameters of a connected graph $G$, the $r$-, $g$-, and $u$-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices $n$ and the diameter $d$ of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the $r$-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the $r$-critical pebbling number is $2^d$.Comment: 26 page

As endemias rurais na Folha SA.22 Belém, do projeto RADAM

Utilizando dados sobre as endemias rurais ou seus vetores e os mapas geológico, geomorfológico e de vegetação, foi possível separar áreas onde essas endemias podem ou não ocorrer. A malária não ocorre num tipo de chapada e noutro de várzea. Só estará livre de leishmaniose muco-cutânea a floresta da placínie aluvial. Já a cutânea difusa é restrita a algumas matas de várzea. Os caramujos hospedeiros intermediários da esquitossomose poderão aparecer, depois do desmatamento, em todas as áreas não sujeitas a inundação. A febre amarela tem ocorrido em todas as florestas e até nas matas ciliares das zonas campestres.<br>Using data from endemic diseases from rural areas and their vectors and geologic, geomorphological and vegetation maps it was possible to plot areas where these diseases are possible to occur. Malaria is not found in one type of plateau and in another type of floodplain. Only the floodplains are free of muco-cutaneous leishmaniasis and the diffuse cutaneous form is restricted to some floodplains forest. Snail intermediate host of schistosomiasis can appear, after deforestation, in all areas presently not periodically flooded. Yellow fever has been found in all forest types, including the gallery forest of grasland zones