Opuscula Math. 38, no. 6 (2018), 841-847
https://doi.org/10.7494/OpMath.2018.38.6.841

Opuscula Mathematica

# Hubtic number in graphs

Sultan Senan Mahde

Abstract. The maximum order of partition of the vertex set $$V(G)$$ into hub sets is called hubtic number of $$G$$ and denoted by $$\xi(G)$$. In this paper we determine the hubtic number of some standard graphs. Also we obtain bounds for $$\xi(G)$$. And we characterize the class of all $$(p,q)$$ graphs for which $$\xi(G)=p$$.

Keywords: hubtic number, hub number, partition.

Mathematics Subject Classification: 05C40, 05C99.

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• Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru - 570 006, India
• Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru - 570 006, India
• Sultan Senan Mahde
• Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru - 570 006, India
• Communicated by Adam Paweł Wojda.
• Revised: 2018-03-22.
• Accepted: 2018-03-29.
• Published online: 2018-07-05.