Minimal least eigenvalue of connected graphs of order n and size m = n + k (5 ⩽ k ⩽ 8)
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DOI: 10.1007/s11464-019-0805-5
Abstract: The least eigenvalue of a connected graph is the least eigenvalue of its adjacency matrix. We characterize the connected graphs of order n and size n + k (5 ⩽ k ⩽ 8 and n… read more here.
Keywords: least eigenvalue; eigenvalue connected; minimal least; graphs order ... See more keywords
All graphs of order n ≥ 11 and diameter 2 with partition dimension n − 3
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DOI: 10.1016/j.heliyon.2020.e03694
Abstract: All graphs of order n with partition dimension 2, n−2, n−1, or n have been characterized. However, finding all graphs on n vertices with partition dimension other than these above numbers is still open. In… read more here.
Keywords: order diameter; partition dimension; partition; graphs order ... See more keywords
On connected graphs of order n with girth g and nullity n − g
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DOI: 10.1016/j.laa.2021.07.005
Abstract: Abstract Let G be a simple graph of order n. The nullity of a graph G, denoted by η ( G ) , is the multiplicity of 0 as an eigenvalue of its adjacency matrix.… read more here.
Keywords: girth; cycle; connected graphs; nullity ... See more keywords