Graphs with large Steiner number

  • J. John Department of Mathematics, Government College of Engineering, Tirunelveli, India
  • M. S. Malchijah Raj Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu, India
Keywords: Steiner distance, Steiner set, Steiner number

Abstract

UDC 519.1

In 2002, Gary Chartrand and Ping Zhang [The Steiner number of a graph, Discrete Math., 242, 41--54 (2002)] characterized the connected graphs $G$ of order $p \geq 3$ with Steiner number $p$, $p-1,$ or $2.$  In our paper, we characterize all connected graphs $G$ of order $p \geq 4$ with Steiner number  $s(G)=p-2$.  In addition, we obtain some sharp Nordhaus–Gaddum bounds for the Steiner number of connected graphs whose complement is also connected.

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Published
02.06.2024
How to Cite
John, J., and M. S. M. Raj. “Graphs With Large Steiner Number”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, no. 5, June 2024, pp. 719 -27, doi:10.3842/umzh.v76i5.7409.
Section
Research articles