Details

Autor(en) / Beteiligte

• G Priscilla Pacifica
• K Christy Rani

Titel

Forcing vertex square free detour number of a graph

Ist Teil von

• Ratio mathematica, 2023-01, Vol.45

Ort / Verlag

Pescara: Accademia Piceno Aprutina dei Velati in Teramo (APAV)

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Electronic Journals Library

Beschreibungen/Notizen

• 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\leα\le\beta and \beta\geq2 for some vertex u in G.