1. Mathematical aspects of Wiener indexMartin Knor, Riste Škrekovski, Aleksandra Tepeh, 2016, original scientific article Abstract: The Wiener index (i.e., the total distance or the transmission number), defined as the sum of distances between all unordered pairs of vertices in a graph, is one of the most popular molecular descriptors. In this article we summarize some results, conjectures and problems on this molecular descriptor, with emphasis on works we were involved in.
Keywords: Wiener index, total distance, topological index, molecular descriptor, chemical graph theory
Published in RUP: 02.01.2022; Views: 2061; Downloads: 46
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2. On minimal forbidden subgraphs for the class of EDM-graphsGašper Jaklič, Jolanda Modic, 2015, original scientific article Abstract: In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. Graphs, for which the distance matrix is not an EDM (NEDM-graphs), are studied. All simple connected non-isomorphic graphs on ▫$n \le 8$▫ nodes are analysed and a characterization of the smallest NEDM-graphs, i.e., the minimal forbidden subgraphs, is given. It is proven that bipartite graphs and some subdivisions of the smallest NEDM-graphs are NEDM-graphs, too.
Keywords: graph theory, graph, Euclidean distance matrix, distance, eigenvalue
Published in RUP: 30.12.2021; Views: 1318; Downloads: 21
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3. Edge-contributions of some topological indices and arboreality of molecular graphsTomaž Pisanski, Janez Žerovnik, 2009, original scientific article Abstract: Some graph invariants can be computed by summing certain values, called edge-contributions over all edges of graphs. In this note we use edge-contributions to study relationships among three graph invariants, also known as topological indices in mathematical chemistry: Wiener index, Szeged index and recently introduced revised Szeged index. We also use the quotient between the Wiener index and the revised Szeged index to study tree-likeness of graphs.
Keywords: mathematical chemistry, chemical graph theory, topological index, revised Szeged index
Published in RUP: 30.12.2021; Views: 1541; Downloads: 20
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6. Parallelizing an algorithm to find the maximal clique on interval graphs on graphical processing unitsChristian Trefftz, Andrés Santamaría-Galvis, Roberto Cruz Rodes, 2014, published scientific conference contribution Keywords: graph theory, graphics processing units, parallel algorithms, CUDA, Thrust library, interval graphs, maximal clique
Published in RUP: 18.10.2021; Views: 1575; Downloads: 24
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10. Reachability relations in digraphsAleksander Malnič, Dragan Marušič, Norbert Seifter, Primož Šparl, Boris Zgrablić, 2008, original scientific article Abstract: In this paper we study reachability relations on vertices of digraphs, informally defined as follows. First, the weight of a walk is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed in the direction opposite to their orientation. Then, a vertex ▫$u$▫ is ▫$R_k^+$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at u has weight in the interval ▫$[0,k]$▫. Similarly, a vertex ▫$u$▫ is ▫$R_k^-$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at ▫$u$▫ has weight in the interval ▫$[-k,0]$▫. For all positive integers ▫$k$▫, the relations ▫$R_k^+$▫ and ▫$R_k^-$▫ are equivalence relations on the vertex set of a given digraph. We prove that, for transitive digraphs, properties of these relations are closely related to other properties such as having property ▫$\mathbb{Z}$▫, the number of ends, growth conditions, and vertex degree.
Keywords: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth
Published in RUP: 02.04.2017; Views: 3228; Downloads: 137
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