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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
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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
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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
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