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The palette index of some Cartesian products of graphs
Full text linkThe palette of a vertex v in a graph is the set of colors assigned to the edges incident to . The palette index of is the minimum number of distinct palettes among the vertices, taken over all proper edge colorings of . This paper presents results on the palette index of the Cartesian product , where one of the factor graphs is a path or a cycle. Additionally, it provides exact results and bounds on the palette index of the Cartesian product of two graphs, where one factor graph is isomorphic to a regular or class nearly regular graph
Razprave Matematično prirodoslovnega razreda Akademije znanosti in umetnosti v Ljubljani
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Kako vegetacija spreminja lastnosti dežnih kapljic
Full text linkThe process of rainfall interception is an important part of the hydrological cycle in many regions. The rainfall which is intercepted by vegetation evaporates into the atmosphere, while throughfall and stemflow contribute to runoff generation, control soil moisture and affect soil erosion. These topics are closely connected to the aims of the ongoing bilateral research project between University of Ljubljana, Slovenian Forestry Institute and TU Wien. The project focuses on the understanding of the effect of meteorological and vegetation characteristics on changes in raindrop microstructure. The rain drop diameter and velocity of raindrops under vegetation, which reach the ground by dripping from leaves and branches as throughfall, are different than diameter and velocity of rain drops above the canopy.Proces prestrezanja padavin je pomemben del hidrološkega kroga v mnogih regijah. Padavine, ki jih prestreže vegetacija, izhlapijo v ozračje, medtem ko padavine, ki prehajajo skozi vegetacijo, uravnavajo vlažnost tal in vplivajo na erozijo tal. Te vsebine so tesno povezane s cilji bilateralnega raziskovalnega projekta med Univerzo v Ljubljani, Slovenskim gozdarskim inštitutom in Tehniško univerzo na Dunaju. Projekt se osredotoča na razumevanje vpliva meteoroloških in vegetacijskih značilnosti na spremembe mikrostrukture dežnih kapljic. Premer in hitrost dežnih kapljic pod vegetacijo, ki dosežejo tla s kapljanjem z listov in vej kot prepuščene padavine, se razlikujeta od premera in hitrosti dežnih kapljic nad krošnjami
S-packing chromatic critical graphs
Full text linkFor a non-decreasing sequence of positive integers , the -packing chromatic number of a graph is denoted by . In this paper, -critical graphs are introduced as the graphs such that for each proper subgraph of . Several families of -critical graphs are constructed, and - and -colorable -critical graphs are presented for all packing sequences , while -colorable -critical graphs are found for most of . Cycles which are -critical are characterized under different conditions. It is proved that for any graph and any edge , the inequality holds. Moreover, in several important cases, this bound can be improved to . The sharpness of the bounds is also discussed. Along the way an earlier result on -vertex-critical graphs is supplemented
Enumerating the number of -matchings in successively amalgamated graphs
Full text linkIn this paper, the transfer matrix technique using the -matching vector is developed to compute the number of -matchings in an arbitrary graph which can be constructed by successive amalgamations over sets of cardinality two. This widely extends known methods from the literature developed for computing the number of -matchings in benzenoid chains, octagonal chains, cyclooctatetraene chains, and arbitrary cyclic chains. Two examples demonstrating how the present method can be applied are given, one of them being an elaborated chemical example
On reduced Hamilton walks
Full text linkA Hamilton walk in a finite graph is a walk, either open or closed, that traverses every vertex at least once. Here, we introduce Hamilton walks that are reduced in the sense that they avoid immediate backtracking: a reduced Hamilton walk never traverses the same edge forth and back consecutively. While every connected graph admits a Hamilton walk, existence of a reduced Hamilton walk is not guaranteed for all graphs. However, we prove that a reduced Hamilton walk does exist in a connected graph with minimal valency at least . Furthermore, given such a graph on vertices, we present an -time algorithm that constructs a reduced Hamilton walk of length at most . Specifically, for a graph belonging to a family of regular expander graphs, we can find a reduced Hamilton walk of length at most , where is a constant independent of
Multilevel toxicity assessment of polypropylene microplastics and pyrene on mussels
Full text linkDespite extensive research on microplastic pollution, combined biological effects of microplastics and associated pollutants on marine invertebrates remain unclear. We present an integrative assessment of polypropylene (PP) and pyrene, individually and in co-exposure, in mussel Mytilus galloprovincialis. Mussels were exposed to 1 mg L−1 PP (~40 μm) and 50 μg L−1 of pyrene for 7 and 14 days, representing a scenario relevant to highly polluted coastal areas. DNA damage increased significantly in mussels exposed to pyrene or PP alone, but remained at control levels under combined exposure, suggesting an interaction that may reduce genotoxic potential. Lipid peroxidation remained stable across treatments, despite significant changes in antioxidant enzymes. Catalase activity increased in pyrene and pyrene + PP treatments, with tissue-specific trends, indicating enhanced antioxidant protection. Glutathione S-transferase activity was stable in digestive glands but significantly inhibited in gills after seven days under PP exposure. ETS activity increased in pyrene-containing treatments after 14 days, reflecting elevated metabolic demand after prolonged exposure. Respiration rate declined under PP exposure. Heart rate recovery time after the hyposalinity test was the slowest in the pyrene + PP group, indicating compromised physiological resilience. These findings reveal interactive, tissue- and biomarker-specific effects of PP and pyrene. Their combination suggested attenuation of genotoxicity but enhanced physiological stress responses, highlighting the complexity of pollutant interactions and importance of evaluating multiple biomarkers, tissues and pollutants. Presented data provide the first ever biomarker-based evaluation of PP and pyrene co-exposure, offering novel insights into microplastic-pollutant interactions and potential ecological consequences for marine invertebrates