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1.
The Hosoya-Wiener polynomial of weighted trees
Blaž 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: 05.07.2017; Ogledov: 584; Prenosov: 58
.pdf Celotno besedilo (182,69 KB)
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2.
Computing the weighted Wiener and Szeged number on weighted cactus graphs in linear time
Blaž Zmazek, Janez Žerovnik, 2003, izvirni znanstveni članek

Opis: Cactus is a graph in which every edge lies on at most one cycle. Linear algorithms for computing the weighted Wiener and Szeged numbers on weighted cactus graphs are given. Graphs with weighted vertices and edges correspond to molecular graphs with heteroatoms.
Ključne besede: mathematics, graph theory, Wiener number, Szeged number, weighted cactus, linear algorithm
Objavljeno: 05.07.2017; Ogledov: 365; Prenosov: 69
.pdf Celotno besedilo (130,41 KB)
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3.
Recognizing weighted directed Cartesian graph bundles
Blaž 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: 31.03.2017; Ogledov: 609; Prenosov: 288
.pdf Celotno besedilo (240,86 KB)
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