Edge-pancyclicity of pancake graph

Chun Nan Hung; Mohamad Abdallah; Jui I. Weng; Tzu Liang Kung

doi:10.1080/23799927.2020.1803972

Edge-pancyclicity of pancake graph

Chun Nan Hung, Mohamad Abdallah, Jui I. Weng, Tzu Liang Kung

Mathematic and Natural Sciences

Research output: Contribution to journal › Review article › peer-review

3 Scopus citations

Abstract

Pancylicity was introduced by Bondy in 1971. A graph G with vertex set (Formula presented.) and edge set (Formula presented.) is pancyclic if it contains cycles of lengths l, for (Formula presented.). This concept has been extended to edge-pancyclicity. If every edge of G is in a cycle of every length, G is edge-pancyclic. If every edge lies on cycles of all lengths ranging from k to (Formula presented.), G is k-edge-pancyclic. In this paper, we prove that the n-dimensional pancake graph is 7-edge-pancyclic.

Original language	English
Pages (from-to)	125-133
Number of pages	9
Journal	International Journal of Computer Mathematics: Computer Systems Theory
Volume	5
Issue number	3
DOIs	https://doi.org/10.1080/23799927.2020.1803972
State	Published - 2 Jul 2020

Keywords

Cayley graph
Pancake graph
cycle embedding
edge-pancylicity
interconnection network

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10.1080/23799927.2020.1803972

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title = "Edge-pancyclicity of pancake graph",

abstract = "Pancylicity was introduced by Bondy in 1971. A graph G with vertex set (Formula presented.) and edge set (Formula presented.) is pancyclic if it contains cycles of lengths l, for (Formula presented.). This concept has been extended to edge-pancyclicity. If every edge of G is in a cycle of every length, G is edge-pancyclic. If every edge lies on cycles of all lengths ranging from k to (Formula presented.), G is k-edge-pancyclic. In this paper, we prove that the n-dimensional pancake graph is 7-edge-pancyclic.",

keywords = "Cayley graph, Pancake graph, cycle embedding, edge-pancylicity, interconnection network",

author = "Hung, \{Chun Nan\} and Mohamad Abdallah and Weng, \{Jui I.\} and Kung, \{Tzu Liang\}",

note = "Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2020",

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doi = "10.1080/23799927.2020.1803972",

language = "English",

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TY - JOUR

T1 - Edge-pancyclicity of pancake graph

AU - Hung, Chun Nan

AU - Abdallah, Mohamad

AU - Weng, Jui I.

AU - Kung, Tzu Liang

PY - 2020/7/2

Y1 - 2020/7/2

N2 - Pancylicity was introduced by Bondy in 1971. A graph G with vertex set (Formula presented.) and edge set (Formula presented.) is pancyclic if it contains cycles of lengths l, for (Formula presented.). This concept has been extended to edge-pancyclicity. If every edge of G is in a cycle of every length, G is edge-pancyclic. If every edge lies on cycles of all lengths ranging from k to (Formula presented.), G is k-edge-pancyclic. In this paper, we prove that the n-dimensional pancake graph is 7-edge-pancyclic.

AB - Pancylicity was introduced by Bondy in 1971. A graph G with vertex set (Formula presented.) and edge set (Formula presented.) is pancyclic if it contains cycles of lengths l, for (Formula presented.). This concept has been extended to edge-pancyclicity. If every edge of G is in a cycle of every length, G is edge-pancyclic. If every edge lies on cycles of all lengths ranging from k to (Formula presented.), G is k-edge-pancyclic. In this paper, we prove that the n-dimensional pancake graph is 7-edge-pancyclic.

KW - Cayley graph

KW - Pancake graph

KW - cycle embedding

KW - edge-pancylicity

KW - interconnection network

UR - https://www.scopus.com/pages/publications/85089441994

U2 - 10.1080/23799927.2020.1803972

DO - 10.1080/23799927.2020.1803972

M3 - Review article

AN - SCOPUS:85089441994

SN - 2379-9927

VL - 5

SP - 125

EP - 133

JO - International Journal of Computer Mathematics: Computer Systems Theory

JF - International Journal of Computer Mathematics: Computer Systems Theory

IS - 3

ER -

Edge-pancyclicity of pancake graph

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