Wiener-type invariants on graph properties

Qiannan Zhou; Ligong Wang; Yong Lu

doi:10.2298/FIL1802489Z

Wiener-type invariants on graph properties

Qiannan Zhou
, Ligong Wang
, Yong Lu

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

4 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 mainly give some sufficient conditions for a connected graph to be k-connected, β-deficient, k-hamiltonian, k-edge-hamiltonian, k-path-coverable or satisfy α(G) ≤ k.

Original language	English
Pages (from-to)	489-502
Number of pages	14
Journal	Filomat
Volume	32
Issue number	2
DOIs	https://doi.org/10.2298/FIL1802489Z
State	Published - 2018

Keywords

Degree sequence
Graph properties
Wiener-type index

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10.2298/FIL1802489Z

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T1 - Wiener-type invariants on graph properties

AU - Zhou, Qiannan

AU - Wang, Ligong

AU - Lu, Yong

PY - 2018

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N2 - 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 mainly give some sufficient conditions for a connected graph to be k-connected, β-deficient, k-hamiltonian, k-edge-hamiltonian, k-path-coverable or satisfy α(G) ≤ k.

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 mainly give some sufficient conditions for a connected graph to be k-connected, β-deficient, k-hamiltonian, k-edge-hamiltonian, k-path-coverable or satisfy α(G) ≤ k.

KW - Degree sequence

KW - Graph properties

KW - Wiener-type index

UR - https://www.scopus.com/pages/publications/85048000288

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DO - 10.2298/FIL1802489Z

M3 - 文章

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SN - 0354-5180

VL - 32

SP - 489

EP - 502

JO - Filomat

JF - Filomat

IS - 2

ER -

Wiener-type invariants on graph properties

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Keywords

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