Spectral extrema of graphs with bounded clique number and matching number

Article Mathematics, Applied

Spectral radius conditions for the existence of all subtrees of diameter at most four

Xiangxiang Liu et al.

Summary: We partly confirm a conjecture by Nikiforov, which is a spectral radius analogue of the Erdos-Sos Conjecture. We prove that for trees with diameter at most four, except for one exception, for k ≥ 8, if a graph G with sufficiently large order n satisfies mu(G) ≥ mu(S-n,S-k) and G is not equal to S-n,S-k, then G contains all trees of order 2k + 3.

LINEAR ALGEBRA AND ITS APPLICATIONS (2023)

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Article Mathematics

The spectral radius of graphs with no odd wheels

Sebastian Cioaba et al.

Summary: This paper investigates the largest value of the spectral radius of the adjacency matrix in an n-vertex graph that does not contain the specific graph W2k+1 for different values of k. The structure of spectral extremal graphs is determined for all k >= 2, excluding k = 4, 5. It is shown that when k is small, there is overlap between the spectral extremal graphs and Turan-extremal graphs, but when k is large, these two families of graphs are disjoint.

EUROPEAN JOURNAL OF COMBINATORICS (2022)

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Article Mathematics, Applied

Spectral radius, edge-disjoint cycles and cycles of the same length

Huiqiu Lin et al.

Summary: This paper provides spectral conditions for the existence of two edge-disjoint cycles and two cycles of the same length in a graph, and a spectral condition to guarantee the existence of k edge-disjoint triangles.

ELECTRONIC JOURNAL OF COMBINATORICS (2022)

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Article Mathematics

Spectral extrema of Ks,t-minor free graphs - On a conjecture of M. Tait

Mingqing Zhai et al.

Summary: This paper focuses on the spectral extrema of K-s,K-t-minor free graphs and determines the extremal graphs with maximum spectral radius among all K-s,K-t-minor free graphs of sufficiently large order. The results generalize and improve previous findings, solving conjectures and providing spectral analogues of theorems. Spectral and structural tools are used to characterize the properties of extremal graphs.

JOURNAL OF COMBINATORIAL THEORY SERIES B (2022)

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Article Mathematics

The spectral radius of graphs without trees of diameter at most four

Xinmin Hou et al.

Summary: The author proved that Nikiforov's conjecture holds true for trees with a diameter at most four, showing that for specific n and k, a graph satisfying mu(G) = mu(S-n,S-k) contains all trees of order 2k+2 with a diameter at most four.

LINEAR & MULTILINEAR ALGEBRA (2021)

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Article Mathematics, Applied