Forcing vertex square free detour number of a graph

Authors

  • G Priscilla Pacifica
  • K Christy Rani

DOI:

https://doi.org/10.23755/rm.v45i0.1030

Keywords:

forcing square free detour number, forcingvertex square free detour set, forcingvertex square free detour number.

Abstract

Let G be a connected graph and S a square free detour basis of G. A subset T\subseteq S is called a forcing subset for S if S is the unique square free detour basis of S containing T. A forcing subset for S of minimum order is a minimum forcing subset of G. The forcing square free detour number of G is fdn◻fu(G)=minfdn◻fuSu, where the minimum is taken over all square free detour bases S in G. In this paper, we introduce the forcing vertex square free detour sets. The general properties satisfied by these forcing subsets are discussed and the forcing square free detour number for a certain class of standard graphs are determined. We show that the two parameters dn◻fu(G) and fdn◻fu(G) satisfy the relationship 0\le fdn◻fu(G)≤dn◻fu(G). Also, we prove the existence of a graph G with fdn◻fu(G)=α and dn◻fu(G)=β, where 0\le\alpha\le\beta and \beta\geq2 for some vertex u in G.

References

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Ramalingam, S. S., Asir, I. K., &Athisayanathan, S. (2017). Upper Vertex Triangle Free Detour Number of a Graph. Mapana Journal of Sciences, 16(3), 27-40.

Ramalingam, S. Sethu, I. Keerthi Asir, and S. Athisayanathan. Vertex Triangle Free Detour Number of a Graph. Mapana Journal of Sciences 15.3 (2016): 9-24.

Santhakumaran, A. P., and S. Athisayanathan. On the connected detour number of a graph.Journal of Prime research in Mathematics 5 (2009): 149-170.

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Published

2023-01-30

Issue

Vol. 45 (2023): Special Issue: Advances in Applied and Intellectual Mathematics

Section

Volume 44-2022

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