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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Graphs with odd and even distances between non-cut vertices
    (Wydawnictwa AGH, 2025) Antoshyna,Kateryna; Kozerenko, Sergiy
    We prove that in a connected graph, the distances between non-cut vertices are odd if and only if it is the line graph of a strong unique independence tree. We then show that any such tree can be inductively constructed from stars using a simple operation. Further, we study the connected graphs in which the distances between non-cut vertices are even (shortly, NCE-graphs). Our main results on NCE-graphs are the following: we give a criterion of NCE-graphs, show that any bipartite graph is an induced subgraph of an NCE-graph, characterize NCE-graphs with exactly two leaves, characterize graphs that can be subdivided to NCE-graphs, and provide a characterization for NCE-graphs which are maximal with respect to the edge addition operation
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Zagrożenia osuwiskowe w Zakładzie Górniczym KWB Bełchatów w trakcie prowadzenia eksploatacji w najgłębszej części złoża, w rowie II rzędu
    (Wydawnictwa AGH, 2011) Sędor, Aleksandra; Czarnecki, Leopold
    In this article described landslide hazards occur while mine technology for extraction in II order graben, the deepest part of the brown coal deposit Bełchatów. Discussed major tectonic structure have influence to safe mine extraction. The article contains precise characteristic fault line called »North border fault line« (UNB no. 2) documented while mine extractions. Drop has been recorded in the Mesozoic substratum and amount 60 to 200 meters. The style of zone is varied from expansive flexure to series fault lines varied angle and dip direction. Interest aspect of this zone is appearing more often imply surfaces in the north side of fault line. The second important aspect described in this article is block of Mesozoic rock which is building south border Kleszczow graben. The zone called paleolandslide block (BP) is locating in the south border fault line Kleszczow graben called USB no. 1. Paleolandslide block is 1700 meters long and it is probably blocks group move to the north board fault line USB no. 1 about 140 meters bring about old landslide. Estimate volume BP is 118 mln $m^{3}$ with documented depth 260 meters. In the board BP charted 11 lower block group deposit in the Tertiary sediments. Described results previous field work driving to better knowledge deformations inside BP. It was taken note of practical aspect recognition structure cause steady inside block as necessary element to right planning and safe mining extraction.