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Graphs with given number of cut-edges and minimal value of Wiener number
Petra Šparl, Janez Žerovnik, 2011, original scientific article

Abstract: A new graph operation is proposed which generalizes two operatins by Hua and its usability is illustrated by proving a theorem which characterizes the graphs with given number of cut-edges and minimal value of the Wiener number.
Keywords: kemijska teorija grafov, topološki indeksi, Wienerjevo število, chemical graph theory, topological indices, Wiener number
Published: 10.07.2015; Views: 469; Downloads: 18
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A theorem on Wiener-type invariants for isometric subgraphs of hypercubes
Sandi Klavžar, Ivan Gutman, 2006, original scientific article

Abstract: Naj bo ▫$d(G,k)$▫ število parov točk grafa ▫$G$▫, ki so na razdalji ▫$k$▫, naj bo ▫$lambda$▫ realno (ali kompleksno) število in naj bo ▫$W_lambda(G) =sum_{k ge 1}d(G,k)k^lambda$▫. Dokazano je, da za delno kocko ▫$G$▫ velja ▫$W_{lambda + 1}(G) = |mathcal{F}| W_lambda(G) - sum_{mathnormal{F} in mathcal{F}} W_lambda(G setminus F)$▫, kjer je ▫$mathcal{F}$▫ particija ▫$E(G)$▫, ki jo inducira Djokovic-Winklerjeva relacija ▫$Theta$▫. Ta rezultat razširja prej znani rezultat za drevesa in implicira različne relacije za topološke indekse, ki temeljijo na razdaljah.
Keywords: matematika, teorija grafov, grafovska razdalja, hiperkocka, delna kocka, Wienerjevo število, hiper-Wienerjev indeks, mathematics, graph theory, graph distance, hypercube, partial cube, Wiener number, hyper-Wiener indeks
Published: 10.07.2015; Views: 491; Downloads: 48
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Computing the weighted Wiener and Szeged number on weighted cactus graphs in linear time
Blaž Zmazek, Janez Žerovnik, 2003, original scientific article

Abstract: 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.
Keywords: mathematics, graph theory, Wiener number, Szeged number, weighted cactus, linear algorithm
Published: 05.07.2017; Views: 191; Downloads: 50
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Wiener numbers of pericondensed benzenoid hydrocarbons
Sandi Klavžar, Ivan Gutman, Amal Rajapakse, 1997, original scientific article

Abstract: Using a recently developed technique for the calculation of the Wiener number (W) of benzenoid systems, we determine explicit expressions for W for several homologous series of pericondensed benzenoid hydrocarbons. An elementary proof for the correctness of the used method is also included.
Keywords: mathematics, chemical graph theory, distance in graphs, Wiener number, benzenoids
Published: 05.07.2017; Views: 356; Downloads: 50
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