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2. The Hosoya-Wiener polynomial of weighted treesBlaž Zmazek, Janez Žerovnik, 2007, izvirni znanstveni članek Opis: 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.
Ključne besede: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs
Objavljeno v DKUM: 05.07.2017; Ogledov: 1394; Prenosov: 116
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4. Recognizing weighted directed Cartesian graph bundlesBlaž Zmazek, Janez Žerovnik, 2000, izvirni znanstveni članek Opis: 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
Ključne besede: mathematics, graph theory, graph bundles, Cartesian graph product, weighted digraphs, half-convexity
Objavljeno v DKUM: 31.03.2017; Ogledov: 1303; Prenosov: 403
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5. 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, recenzija, prikaz knjige, kritika Ključne besede: matematika, kemijska teorija grafov, lastna vrednost, Laplaceova matrika, utežen graf, mathematics, chemical graph theory, eigenvalue, Laplacian matrix, weighted graph
Objavljeno v DKUM: 10.07.2015; Ogledov: 37382; Prenosov: 21
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6. 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, recenzija, prikaz knjige, kritika Ključne besede: matematika, teorija grafov, računalništvo, stopnja aproksimacije, problem maksimizacije, mathematics, graph theory, computer science, weighted hereditary induced-subgraph maximization problems
Objavljeno v DKUM: 10.07.2015; Ogledov: 868; Prenosov: 33
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