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On split graphs with three or four distinct (normalized) Laplacian eigenvalues
Author(s) -
Li Shuchao,
Sun Wanting
Publication year - 2020
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21743
Subject(s) - mathematics , combinatorics , laplace operator , laplacian matrix , eigenvalues and eigenvectors , vertex (graph theory) , resistance distance , graph , laplacian smoothing , discrete mathematics , line graph , graph power , mathematical analysis , physics , finite element method , mesh generation , thermodynamics , quantum mechanics
It is well known to us that a graph of diameter l has at least l + 1 eigenvalues. A graph is said to be Laplacian (resp, normalized Laplacian ) l ‐ extremal if it is of diameter l having exactly l + 1 distinct Laplacian (resp, normalized Laplacian) eigenvalues. A graph is split if its vertex set can be partitioned into a clique and a stable set. Each split graph is of diameter at most 3. In this paper, we completely classify the connected bidegreed Laplacian (resp, normalized Laplacian) 2‐extremal (resp, 3‐extremal) split graphs using the association of split graphs with combinatorial designs. Furthermore, we identify connected bidegreed split graphs of diameter 2 having just four Laplacian (resp, normalized Laplacian) eigenvalues.