The number of dominating k-sets of paths, cycles and wheels

2016/01/06 by Jorge L. Arocha, Arocha, Jorge L., Bernardo Llano +1
Mathematics · #05C30 #05C69 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C30 #msc:05C69

paper · pdf · doi:10.48550/arxiv.1601.01268

13 pages

arxiv created 2016/01/06 · arxiv updated 2016/01/07

Abstract

We give a shorter proof of the recurrence relation for the domination polynomial γ(P_n,t) and for the number γ_k(P_n) of dominating k-sets of the path with n vertices. For every positive integers n and k, numbers γ_k(P_n) are determined solving a problem posed by S. Alikhani in CID 2015. Moreover, the numbers of dominating k-sets γ_k(C_n) of cycles and γ_k(W_n) of wheels with n vertices are computed.

Related

• The domination polynomial of powers of paths and cycles
• Dominating sets and Domination polynomials of Cycles
• Cycles are determined by their domination polynomials
• Bounding the number of (σ,ρ)-dominating sets in trees, forests and graphs of bounded pathwidth
• Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph