The Crossing Number of Join Product of kth Power of Path Pm with Isolated Vertices and Path Pn

Sun Yuan Hsieh, Cheng Chian Lin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

A graph G is said to have a crossing if two edges of G share an interior point. The minimum crossing number of G is denoted by cr(G). The crossing number problem is to find the minimum crossing solution of a graph, and it can be used in applications of circuit layout. Although the crossing numbers of join product graphs have been extensively studied, the crossing number of join product of power graphs with path is relatively unexplored. Let Pm and Pn be paths with m and n vertices, and Dn be a graph consisting of n isolated vertices. In this paper, we investigate the crossing number of kth power of path Pm that joins with isolated vertices Dn and path Pn. We have proved the minimum crossing numbers of Pk m+Dn for m ≤ 6, n ≥ 1, and Pk m+Pn for m ≤ 6, n ≥ 2.

Original languageEnglish
Title of host publicationProceedings - 2016 International Computer Symposium, ICS 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages62-67
Number of pages6
ISBN (Electronic)9781509034383
DOIs
Publication statusPublished - 2017 Feb 16
Event2016 International Computer Symposium, ICS 2016 - Chiayi, Taiwan
Duration: 2016 Dec 152016 Dec 17

Publication series

NameProceedings - 2016 International Computer Symposium, ICS 2016

Other

Other2016 International Computer Symposium, ICS 2016
CountryTaiwan
CityChiayi
Period16-12-1516-12-17

All Science Journal Classification (ASJC) codes

  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computer Science Applications

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