Log-concavity of the independence polynomials of W_p graphs

2024/09/01 by Hoang, Do Trong, Levit, Vadim E., Mandrescu, Eugen +1 · 1 citation
#05C31 #05C48 (Secondary) #05C69 (Primary) 05C05 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2.1 #G.2.2

paper · doi:10.48550/arxiv.2409.00827

Abstract

Let G be a graph of order n. For a positive integer p, G is said to be a W_p graph if n≥ p and every p pairwise disjoint independent sets of G are contained within p pairwise disjoint maximum independent sets. In this paper, we establish that every connected W_p graph G is p-quasi-regularizable if and only if n≥(p+1)⋅α, where α is the independence number of G and p≠2. This finding ensures that the independence polynomial of a connected W_p graph G is log-concave whenever (p+1)⋅α≤ n≤ p⋅α+2√(p⋅α+p) and \fracα²4( α+1) ≤ p, or p⋅α+2√(p⋅α+p)

Cited by

• Structural properties and characterizations of W_p class

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