Weakly status injective trees are status unique in trees

Jen Ling Shang; Tay Woei Shyu; Chiang Lin

Weakly status injective trees are status unique in trees

Jen Ling Shang^*
, Tay Woei Shyu
, Chiang Lin

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

The status of a vertex x in a graph is the sum of the distances between x and all other vertices. The status sequence of a graph is the list of the statuses of all vertices arranged in nondecreasing order. It is well known that non-isomorphic trees may have the same status sequence. We show that a tree is uniquely determined by its status sequence if the only pairs of vertices that have the same status are endvertices.

Original language	English
Pages (from-to)	133-143
Number of pages	11
Journal	Ars Combinatoria
Volume	139
Publication status	Published - 2018 Jul

Keywords

Status
Status injective graph
Status sequence
Status unique graph
Tree
Weakly status injective tree

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "Weakly status injective trees are status unique in trees",

abstract = "The status of a vertex x in a graph is the sum of the distances between x and all other vertices. The status sequence of a graph is the list of the statuses of all vertices arranged in nondecreasing order. It is well known that non-isomorphic trees may have the same status sequence. We show that a tree is uniquely determined by its status sequence if the only pairs of vertices that have the same status are endvertices.",

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journal = "Ars Combinatoria",

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T1 - Weakly status injective trees are status unique in trees

AU - Shang, Jen Ling

AU - Shyu, Tay Woei

AU - Lin, Chiang

PY - 2018/7

Y1 - 2018/7

N2 - The status of a vertex x in a graph is the sum of the distances between x and all other vertices. The status sequence of a graph is the list of the statuses of all vertices arranged in nondecreasing order. It is well known that non-isomorphic trees may have the same status sequence. We show that a tree is uniquely determined by its status sequence if the only pairs of vertices that have the same status are endvertices.

AB - The status of a vertex x in a graph is the sum of the distances between x and all other vertices. The status sequence of a graph is the list of the statuses of all vertices arranged in nondecreasing order. It is well known that non-isomorphic trees may have the same status sequence. We show that a tree is uniquely determined by its status sequence if the only pairs of vertices that have the same status are endvertices.

KW - Status

KW - Status injective graph

KW - Status sequence

KW - Status unique graph

KW - Tree

KW - Weakly status injective tree

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UR - https://www.scopus.com/pages/publications/85051545469#tab=citedBy

M3 - Article

AN - SCOPUS:85051545469

SN - 0381-7032

VL - 139

SP - 133

EP - 143

JO - Ars Combinatoria

JF - Ars Combinatoria

ER -

Weakly status injective trees are status unique in trees

Abstract

Keywords

ASJC Scopus subject areas

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