1. Mathematical aspects of Wiener indexMartin Knor, Riste Škrekovski, Aleksandra Tepeh, 2016, izvirni znanstveni članek Opis: 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.
Ključne besede: Wiener index, total distance, topological index, molecular descriptor, chemical graph theory
Objavljeno v RUP: 02.01.2022; Ogledov: 2066; Prenosov: 46
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2. On minimal forbidden subgraphs for the class of EDM-graphsGašper Jaklič, Jolanda Modic, 2015, izvirni znanstveni članek Opis: 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.
Ključne besede: graph theory, graph, Euclidean distance matrix, distance, eigenvalue
Objavljeno v RUP: 30.12.2021; Ogledov: 1322; Prenosov: 21
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3. Edge-contributions of some topological indices and arboreality of molecular graphsTomaž Pisanski, Janez Žerovnik, 2009, izvirni znanstveni članek Opis: 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.
Ključne besede: mathematical chemistry, chemical graph theory, topological index, revised Szeged index
Objavljeno v RUP: 30.12.2021; Ogledov: 1545; Prenosov: 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, objavljeni znanstveni prispevek na konferenci Ključne besede: graph theory, graphics processing units, parallel algorithms, CUDA, Thrust library, interval graphs, maximal clique
Objavljeno v RUP: 18.10.2021; Ogledov: 1576; Prenosov: 24
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10. Reachability relations in digraphsAleksander Malnič, Dragan Marušič, Norbert Seifter, Primož Šparl, Boris Zgrablić, 2008, izvirni znanstveni članek Opis: 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.
Ključne besede: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth
Objavljeno v RUP: 02.04.2017; Ogledov: 3228; Prenosov: 137
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