1. The Hosoya-Wiener polynomial of weighted treesBlaž Zmazek, Janez Žerovnik, 2007, original scientific article Abstract: Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given. Keywords: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs Published in DKUM: 05.07.2017; Views: 1394; Downloads: 114 Full text (182,69 KB) This document has many files! More... |
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3. Recognizing weighted directed Cartesian graph bundlesBlaž Zmazek, Janez Žerovnik, 2000, original scientific article Abstract: In this paper we show that methods for recognizing Cartesian graph bundles can be generalized to weighted digraphs. The main result is an algorithm which lists the sets of degenerate arcs for all representations of digraph as a weighted directed Cartesian graph bundle over simple base digraphs not containing transitive tournament on three vertices. Two main notions are used.The first one is the new relation ▫$\vec{\delta}^\ast$▫ defined among the arcs of a digraph as a weighted directed analogue of the well-known relation ▫$\delta^\ast$▫. The second one is the concept of half-convex subgraphs. A subgraph ▫$H$▫ is half-convex in ▫$G$▫ if any vertex ▫$x \in G \setminus H$▫ has at most one predecessor and at most one successor Keywords: mathematics, graph theory, graph bundles, Cartesian graph product, weighted digraphs, half-convexity Published in DKUM: 31.03.2017; Views: 1303; Downloads: 388 Full text (240,86 KB) This document has many files! More... |
4. Li, Hao(PRC-TSI); Lu, Mei(PRC-TSI): The $m$-connectivity index of graphs. (English summary). - MATCH Commun. Math. Comput. Chem. 54 (2005), no. 2, 417--423.Sandi Klavžar, 2006, review, book review, critique Keywords: matematika, kemijska teorija grafov, lastna vrednost, Laplaceova matrika, utežen graf, mathematics, chemical graph theory, eigenvalue, Laplacian matrix, weighted graph Published in DKUM: 10.07.2015; Views: 37382; Downloads: 20 Link to full text |
5. Demange, Marc; Paschos, Vangelis (F-PARIS9-LA): Improved approximations for weighted and unweighted graph problems. (English. English summary. - Theory Comput. Syst. 38 (2005), no. 6, 763--787.Aleksander Vesel, 2006, review, book review, critique Keywords: matematika, teorija grafov, računalništvo, stopnja aproksimacije, problem maksimizacije, mathematics, graph theory, computer science, weighted hereditary induced-subgraph maximization problems Published in DKUM: 10.07.2015; Views: 868; Downloads: 32 Link to full text |