Signless Laplacian spectral conditions for Hamilton-connected graphs with large minimum degree

Zhou, Qing; Wang, Ligong; Lu, Yilong

doi:10.1016/j.laa.2020.01.021

Cited by 12 publications

(5 citation statements)

References 22 publications

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“…Recently, Chen et al [37], Yu et al [178], and Wei et al [169] independently showed the spectral version of Hamilton-connectedness for graphs with large minimum degree. In 2020, Zhou, Wang and Lu [199] presented the signless Laplacian spectral conditions for Hamilton-connected graphs with large minimum degree.…”

Section: Problem For K-edge-connectivitymentioning

confidence: 99%

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A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

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This survey is two-fold. We first report new progress on the spectral extremal results on the Turán type problems in graph theory. More precisely, we shall summarize the spectral Turán function in terms of the adjacency spectral radius and the signless Laplacian spectral radius for various graphs. For instance, the complete graphs, general graphs with chromatic number at least three, complete bipartite graphs, odd cycles, even cycles, color-critical graphs and intersecting triangles.The second goal is to conclude some recent results of the spectral conditions on some graphical properties. By a unified method, we present some sufficient conditions based on the adjacency spectral radius and the signless Laplacian spectral radius for a graph to be Hamiltonian, k-Hamiltonian, k-edge-Hamiltonian, traceable, k-pathcoverable, k-connected, k-edge-connected, Hamilton-connected, perfect matching and β-deficient.

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Section: Problem For K-edge-connectivitymentioning

confidence: 99%

“…Moreover, we can verify that δ(G) = δ and q(G) ≥ 2(n − δ) for every G ∈ S (1) n,δ ∪ T (1) n,δ . Theorem 4.30 (Zhou-Wang-Lu [199]). Let δ ≥ 2 and n ≥ n 1 (δ) where n 1 (δ) = δ 4 + 5δ 3 + 2δ 2 + 8δ + 12.…”

Section: Problem For K-edge-connectivitymentioning

confidence: 99%

A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

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“…Hung et al [15] studied Hamilton-connectivity of alphabet grid graphs. Zhou et al [16] extended a result of Fiedler and Nikiforov and derived signless Laplacian spectral conditions for Hamilton-connected graphs with large minimum degree. Recently, Shabbir et al [17] studied Hamilton-connectivity in Teoplitz graphs.…”

Section: Introductionmentioning

confidence: 97%

Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index

Hayat

Khan

et al. 2021

Complexity

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A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.

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“…Zhou and Wang [19] proved a better condition for a graph to be Hamilton-connected: e(G) ≥ n−t 2 +t 2 +t. Recently, Xu, Zhai and Wang [15] improved the results of [5] and [19].…”

Section: Introductionmentioning

confidence: 99%

An improvement of sufficient condition for $k$-leaf-connected graphs

Ma¹,

Ao²,

Liu³

et al. 2022

Preprint

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and given any subset S ⊆ V(G) with |S | = k, G always has a spanning tree T such that S is precisely the set of leaves of T. Thus a graph is 2-leaf-connected if and only if it is Hamilton-connected. In this paper, we present a best possible condition based upon the size to guarantee a graph to be k-leaf-connected, which not only improves the results of Gurgel and Wakabayashi [On k-leaf-connected graphs, J. Combin. Theory Ser. B 41 (1986) 1-16] and Ao, Liu, Yuan and Li [Improved sufficient conditions for k-leafconnected graphs, Discrete Appl. Math. 314 (2022) 17-30], but also extends the result of Xu, Zhai and Wang [An improvement of spectral conditions for Hamilton-connected graphs, Linear Multilinear Algebra, 2021]. Our key approach is showing that an (n+k−1)closed non-k-leaf-connected graph must contain a large clique if its size is large enough. As applications, sufficient conditions for a graph to be k-leaf-connected in terms of the (signless Laplacian) spectral radius of G or its complement are also presented.

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Signless Laplacian spectral conditions for Hamilton-connected graphs with large minimum degree

Abstract: In this paper, we present a spectral sufficient condition for a graph to be Hamilton-connected in terms of signless Laplacian spectral radius with large minimum degree.

Cited by 12 publications

References 22 publications

A survey on spectral conditions for some extremal graph problems

A survey on spectral conditions for some extremal graph problems

Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index

An improvement of sufficient condition for $k$-leaf-connected graphs

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