2023/09/17 by Sizhong Zhou, Yuli Zhang, Zhou, Sizhong +1
Mathematics · Neuroscience · #05C50 #05C70 #05C72 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Nuclear Receptors and Signaling
paper · pdf · doi:10.48550/arxiv.2309.09279
openalex publication_date 2023/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let a and b be two positive integers with a≤ b, and let G be a graph with vertex set V(G) and edge set E(G). Let h:E(G)→[0,1] be a function. If a≤∑e∈ EG(v)h(e)≤ b holds for every v∈ V(G), then the subgraph of G with vertex set V(G) and edge set Fh, denoted by G[Fh], is called a fractional [a,b]-factor of G with indicator function h, where EG(v) denotes the set of edges incident with v in G and Fh=\e∈ E(G):h(e)>0\. A graph G is defined as a fractional [a,b]-deleted graph if for any e∈ E(G), G-e contains a fractional [a,b]-factor. The size, spectral radius and signless Laplacian spectral radius of G are denoted by e(G), ρ(G) and q(G), respectively. In this paper, we establish a lower bound on the size, spectral radius and signless Laplacian spectral radius of a graph G to guarantee that G is a fractional [a,b]-deleted graph.