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Povzetek: A set of edges $X\subseteq E(G)$ of a graph $G$ is an edge general position set if no three edges from $X$ lie on a common shortest path. The edge general position number ${\rm gp}_{\rm e}(G)$ of $G$ is the cardinality of a largest edge general position set in $G$. Graphs $G$ with ${\rm gp}_{\rm e}(G) = |E(G)| - 1$ and with ${\rm gp}_{\rm e}(G) = 3$ are respectively characterized. Sharp upper and lower bounds on ${\rm gp}_{\rm e}(G)$ are proved for block graphs $G$ and exact values are determined for several specific block graphs.
Ključne besede: general position set, edge general position set, cut-vertex, diametral path, block graphs
Objavljeno v DiRROS: 27.03.2024; Ogledov: 107; Prenosov: 46
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Povzetek: The edge-Hosoya polynomial of a graph is the edge version of the famous Hosoya polynomial. Therefore, the edge-Hosoya polynomial counts the number of (unordered) pairs of edges at distance $k \ge 0$ in a given graph. It is well known that this polynomial is closely related to the edge-Wiener index and the edge-hyper-Wiener index. As the main result of this paper, we greatly generalize an earlier result by providing a method for calculating the edge-Hosoya polynomial of a graph $G$ which is obtained by identifying two edges of connected bipartite graphs $G_1$ and $G_2$. To show how the main theorem can be used, we apply it to phenylene chains. In particular, we present the recurrence relations and a linear time algorithm for calculating the edge-Hosoya polynomial of any phenylene chain. As a consequence, closed formula for the edge-Hosoya polynomial of linear phenylene chains is derived.
Ključne besede: edge-Hosoya polynomial, graphs, phenylenes
Objavljeno v DiRROS: 18.03.2024; Ogledov: 87; Prenosov: 29
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Povzetek: A set of vertices $X$ of a graph $G$ is a strong edge geodetic set if to any pair of vertices from $X$ we can assign one (or zero) shortest path between them such that every edge of $G$ is contained in at least one on these paths. The cardinality of a smallest strong edge geodetic set of $G$ is the strong edge geodetic number ${\rm sg_e}(G)$ of $G$. In this paper, the strong edge geodetic number of complete multipartite graphs is determined. Graphs $G$ with ${\rm sg_e}(G) = n(G)$ are characterized and ${\rm sg_e}$ is determined for Cartesian products $P_n\,\square\, K_m$. The latter result in particular corrects an error from the literature.
Ključne besede: strong edge geodetic problem, complete multipartite graph, edge-coloring, Cartesian product of graphs
Objavljeno v DiRROS: 19.02.2024; Ogledov: 144; Prenosov: 49
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Povzetek: In the presented research, we studied the forest edge structure of urban and peri-urban forests on the outskirts of Ljubljana (Slovenia) consisting of a number of patches covering the collective surface of 1884 ha. They differ from each other according to the degree of fragmentation and by the share of the interior forest area. On the basis of LiDAR data, we conducted an analysis of the edges of the persistent forest patches and estimated them with regard to the land use they bordered on. The horizontal estimation of forest edges and the changes of forest edges, in the last decades, were estimated using digital orthophoto images of cyclic aerial surveys of Slovenia, from 1975 to 2018. The data, provided by LiDAR, were used to obtain an accurate estimate of forest edges and the metrics of their vertical canopy structure. On the basis of the canopy height model (CHM), we determined the height classes, the heights of the tallest trees, and indices of canopy height diversity (CHD) as variables subjected to a k-means cluster analysis. To determine the forest edge and trees stability, their heights and diameters at breast height (DBH) were measured and their canopy length and h/d (height/diameter) dimension ratios were estimated. In the study area of the Golovec forest patch, more than half of the forest edge segments (56%) border on residential buildings. After the construction of buildings, 54% of the newly formed forest edges developed a high and steep structure. Unfavorable h/d dimension ratio was estimated for 16% of trees, more among the coniferous than among the deciduous trees. Similar characteristics of newly formed forest edges bordering on built-up areas were determined in other sub-urban forest patches, despite the smaller share of such forest edges (19% and 10%, respectively). Tools and methods presented in the research enable the implementation of concrete silvicultural practices in a realistic time period and extend to ensure that adequate forestry measures are taken to minimize possible disturbances.
Ključne besede: forest ecosystem services, forest edge stability, forest edge structure, LiDAR, urban forests
Objavljeno v DiRROS: 26.05.2020; Ogledov: 1892; Prenosov: 1029
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Povzetek: In most mammalian species, body mass is one of the key factors affecting an individual's fitness. It is therefore important to know the causes of its variability. The present paper analyses the influences of habitat structure and other environmental factors on body mass in red deer. The research is based on data sets concerning 3,920 culled red deer from the entire Slovenia, which are geo-referenced within a kilometer spatial accuracy, and on 28 spatially explicit raster layers of population density, habitat structure variables (e.g. topography, land use, forest structure, roads) and other environmental variables (e.g. air temperature, precipitation, supplementary feeding). After controlling for sex and age of the individual and its date of culling, body weight significantly differs between population areas, most likely as a result of genotype differences and genotype impact on the phenotype, and is also negatively dependent upon population density and the percentage of conifers and positively dependent upon annual mean air temperature and forest/meadow edge density. The stated environmental factors probably influence the achieved energy balance and, therefore, the body mass of red deer by conditioning the quantity and quality of food and energy expenditure of deer.
Ključne besede: red deer, body weight, habitat, evironmental factors, population density, forest edge, conifer, temperature, Slovenia
Objavljeno v DiRROS: 12.07.2017; Ogledov: 4482; Prenosov: 2002
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