2023/10/30 by Tingyan Ma, Ma, Tingyan, Ligong Wang +1
Computer Science · Mathematics · Neuroscience · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Nuclear Receptors and Signaling
paper · pdf · doi:10.48550/arxiv.2310.19259
openalex publication_date 2023/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V(G), E(G)) be a graph with vertex set V(G) and edge set E(G). A graph is ID-factor-critical if for every independent set I of G whose size has the same parity as |V(G)|, G-I has a perfect matching. For two positive integers a and b with a≤ b, let h: E(G)→ [0, 1] be a function on E(G) satisfying a≤∑ _e∈ EG(vi)h(e)≤ b for any vertex vi∈ V(G). Then the spanning subgraph with edge set Eh, denoted by G[Eh], is called a fractional [a, b]-factor of G with indicator function h, where Eh=\e∈ E(G)| h(e)>0\ and EG(vi)=\e∈ E(G)| e is incident with vi in G\. A graph is defined as a fractional [a, b]-deleted graph if for any e∈ E(G), G-e contains a fractional [a, b]-factor. For any integer k≥ 1, a graph has a k-factor if it contains a k-regular spanning subgraph. In this paper, we firstly give a distance spectral radius condition of G to guarantee that G is ID-factor-critical. Furthermore, we provide sufficient conditions in terms of distance spectral radius and distance signless Laplacian spectral radius for a graph to contain a fractional [a, b]-factor, fractional [a, b]-deleted-factor and k-factor.