Forcing vertex square free detour number of a graph

G Priscilla Pacifica, K Christy Rani

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.

Keywords


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

Full Text:

PDF

References


Chartrand, Gary, Garry L. Johns, and Songlin Tian. Detour distance in graphs. Annals of discrete mathematics. Vol. 55. Elsevier (1993): 127-136.

Chartrand, Garry L. Johns and Ping Zhang. The detour number of a graph. Util. Math. 64, (2003): 97-113.

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.




DOI: http://dx.doi.org/10.23755/rm.v45i0.1030

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 G Priscilla Pacifica, K Christy Rani

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.