2023/10/18 by Guragain, Satyam, Srivastava, Ravi
#05C22 #05C50 #15A42 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.11907
This paper explores interlacing inequalities in the Laplacian spectrum of signed cycles and investigates interlacing relationship between the spectrum of the net-Laplacian of a signed graph and its subgraph formed by removing a vertex together with its incident edges. Additionally, an inequality is derived between the net-Laplacian spectrum of a complete co-regular signed graph Γ and the Laplacian spectrum of the graph obtained by removing any vertex v from Γ. Also for a signed graph Γ, the net-Laplacian matrix is normalized and an inequality is derived between the spectrum of the normalized net-Laplacian of a signed graph and its subgraph, formed by contraction of edge and vertex.