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Self $2$-distance Graphs

  Published:2016-11-18
 Printed: Mar 2017
  • Ali Azimi,
    Department of Mathematics, University of Neyshabur, P. O. Box 91136-899, Neyshabur, Iran
  • Mohammad Farrokhi Derakhshandeh Ghouchan,
    Mathematical Science Research Unit, College of Liberal Arts, Muroran Institute of Technology, 27-1, Mizumoto, Muroran 050-8585, Hokkaido, Japan
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Abstract

All finite simple self $2$-distance graphs with no square, diamond, or triangles with a common vertex as subgraph are determined. Utilizing these results, it is shown that there is no cubic self $2$-distance graph.
Keywords: distance graph, regular graph, forbidden subgraph distance graph, regular graph, forbidden subgraph
MSC Classifications: 05C12, 05C60, 05C76 show english descriptions Distance in graphs
Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
Graph operations (line graphs, products, etc.)
05C12 - Distance in graphs
05C60 - Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C76 - Graph operations (line graphs, products, etc.)
 

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