Wiener-type invariants and hamiltonian properties of graphs

Qian Nan Zhou; Li Gong Wang; Yong Lu

doi:10.2298/FIL1913045Z

Wiener-type invariants and hamiltonian properties of graphs

Qian Nan Zhou, Li Gong Wang, Yong Lu

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The Wiener-type invariants of a simple connected graph G = (V(G), E(G)) can be expressed in terms of the quantities W_f =^∑{u,v}⊆V(G) f (d_G (u, v)) for various choices of the function f (x), where d_G (u, v) is the distance between vertices u and v in G. In this paper, we give some sufficient conditions for a bipartite graph to be Hamiltonian or a connected general graph to be Hamilton-connected and traceable from every vertex in terms of the Wiener-type invariants of G or the complement of G.

Original language	English
Pages (from-to)	4045-4058
Number of pages	14
Journal	Filomat
Volume	33
Issue number	13
DOIs	https://doi.org/10.2298/FIL1913045Z
State	Published - 2019

Keywords

Hamilton-connected
Hamiltonian
Traceable from every vertex
Wiener-type invariant

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10.2298/FIL1913045Z

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AU - Zhou, Qian Nan

AU - Wang, Li Gong

AU - Lu, Yong

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AB - The Wiener-type invariants of a simple connected graph G = (V(G), E(G)) can be expressed in terms of the quantities Wf =∑{u,v}⊆V(G) f (dG (u, v)) for various choices of the function f (x), where dG (u, v) is the distance between vertices u and v in G. In this paper, we give some sufficient conditions for a bipartite graph to be Hamiltonian or a connected general graph to be Hamilton-connected and traceable from every vertex in terms of the Wiener-type invariants of G or the complement of G.

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KW - Hamiltonian

KW - Traceable from every vertex

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JO - Filomat

JF - Filomat

IS - 13

ER -

Wiener-type invariants and hamiltonian properties of graphs

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Keywords

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