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Boundary Vertices of Cartesian Product of Directed Graphs

  • Manoj Changat
  • Prasanth G. Narasimha-Shenoi
  • Mary Shalet Thottungal JosephEmail author
  • Ram Kumar
Original Paper
  • 14 Downloads

Abstract

Suppose that \(D=(V,E)\) is a strongly connected digraph. Let \(u, v \in V(D)\). The maximum distance md(uv) defined as \(md(u,v)=max\{\overrightarrow{d}(u,v), \overrightarrow{d}(v,u)\}\) is a metric, where \(\overrightarrow{d}(u,v)\) denote the length of a shortest directed \(u-v\) path in D. The boundary, contour, eccentricity and periphery sets of a strong digraph D are defined with respect to this metric. The main aim of this paper is to identify the above said metrically defined sets of a strong digraph D in terms of its prime factor decomposition with respect to Cartesian product.

Keywords

Maximum distance Boundary Contour Eccentricity Periphery Two sided eccentricity property 

Mathematics Subject Classification

05C20 

Notes

Acknowledgements

Prasanth G. Narasimha-Shenoi and Mary Shalet T. J. are supported by Science and Engineering Research Board, a statutory board of Government of India under their Extra Mural Research Funding No. EMR/2015/002183. Also, their research was partially supported by Kerala State Council for Science Technology and Environment of Government of Kerala under their SARD project grant Council(P) No. 436/2014/KSCSTE. Authors acknowledge the reviewers for their valuable comments and suggestions.

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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  • Manoj Changat
    • 1
  • Prasanth G. Narasimha-Shenoi
    • 2
  • Mary Shalet Thottungal Joseph
    • 2
    Email author
  • Ram Kumar
    • 3
  1. 1.Department of Futures StudiesUniversity of KeralaTrivandrumIndia
  2. 2.Department of MathematicsGovernment College ChitturPalakkadIndia
  3. 3.Department of MathematicsM. G. CollegeTrivandrumIndia

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