On the minimal matching energies of unicyclic graphs

Zhu, Jianming; Yang, Ju Qing

doi:10.1016/j.dam.2018.06.013

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…Recently, some bounds on AG spectral radius and AG energy were obtained in a couple of papers [4,5]. Until now, hundreds of such "energy" have been introduced, such as inverse sum index energy [6], distance energy [7,8], ABC energy [9,10], matching energy [11,12], and Randić energy [13,14]. Recently, there are many studies, such as [15][16][17], on the energy of graphs with given parameters.…”

Section: Introductionmentioning

confidence: 99%

Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

Wang

Gao

2020

Mathematical Problems in Engineering

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Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

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Section: Introductionmentioning

confidence: 99%

Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

Wang

Gao

2020

Mathematical Problems in Engineering

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“…In [31], Gutman and Wagner characterized the unicyclic graphs with the minimal and maximal matching energy. Zhu and Yang [35] determined the unicyclic graphs with the first eight minimal matching energies. In [36], Chen and Liu characterized the bipartite unicyclic graphs with the first ( )…”

Section: Introductionmentioning

confidence: 99%

“…, , , , , , , , , , m G k cannot be compared uniformly, then the common comparing method is invalid, and this happens quite often. Recently much effort has been made to tackle these quasi-order incomparable problems [35] [39] [40].…”

Section: Introductionmentioning

confidence: 99%

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

Zhu¹

2019

OJDM

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In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively.A fundamental problem encountered within the study of graph energy is the characterization of the graphs that belong to a given class of graphs having

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Algorithms for enumerating multiple leaf-distance granular regular α-subtree of unicyclic and edge-disjoint bicyclic graphs

Li,

Yang,

Hui

et al. 2024

Applied Mathematics and Computation

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On the minimal matching energies of unicyclic graphs

Cited by 3 publications

References 11 publications

Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

Algorithms for enumerating multiple leaf-distance granular regular α-subtree of unicyclic and edge-disjoint bicyclic graphs

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