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Distance signless Laplacian eigenvalues of graphs

Frontiers of Mathematics in China 2019年第4期14卷 693-713页

作者： kinkar chandra das Huiqiu LIN Jiming GUO Department of Mathematics Sungkyunkwan University Suwon 16419 Republic of Korea Department of Mat hematics East China University of Science and Technology Shanghai 200237 China

Suppose that the vertex set of a graph G is V(G) ={v1,v2,...,vn}.The transmission Tr(vi) (or Di) of vertex vi is defined to be the sum of distances from vi to all other *** Tr(G) be the n × n diagonal matrix with its (i,i)-entry equal to TrG(vi).The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G,defined as L(G) =Tr(G) + D(G),where D(G) is the distance matrix of *** this paper,we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best *** obtain a lower bound on the second largest distance signless Laplacian eigenvalue of ***,we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees,and characterize extremal graphs.

关键词： Graph distance signless Laplacian spectral radius second largest eigenvalue of distance signless Laplacian matrix spread

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Comparison and Extremal Results on Three Eccentricity-based Invariants of Graphs

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Acta Mathematica Sinica,English Series 2020年第1期36卷 40-54页

作者： Ke Xiang XU kinkar chandra das Xiao Qian GU College of Science Nanjing University of Aeronautics&AstronauticsNanjing 210016P.R.China Department of Mathematics Sungkyunkwan UniversitySuwon 440-746Republic of Korea

The first and second Zagreb eccentricity indices of graph G are defined as:E1(G)=∑(vi)∈V(G)εG(vi)~2,E2(G)=∑(vivj)∈E(G)εG(vi)εG(vj)whereεG(vi)denotes the eccentricity of vertex vi in *** eccentric complexity C(ec)(G)of G is the number of different eccentricities of vertices in *** this paper we present some results on the comparison between E1(G)/n and E2(G)/m for any connected graphs G of order n with m edges,including general graphs and the graphs with given C(ec).Moreover,a Nordhaus-Gaddum type result C(ec)(G)+C(ec)(■)is determined with extremal graphs at which the upper and lower bounds are attained respectively.

关键词： Eccentricity(of vertex) first Zagreb eccentricity index second Zagreb eccentricity index eccentric complexity diameter

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Comparison between Merrifield–Simmons Index and Wiener Index of Graphs

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Acta Mathematica Sinica,English Series 2022年第12期38卷 2220-2230页

作者： Ke Xiang XU kinkar chandra das Ivan GUTMAN Meng Lu WANG College of Mathematics Nanjing University of Aeronautics&AstronauticsNanjing 210016P.R.China MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles Nanjing 210016P.R.China Department of Mathematics Sungkyunkwan UniversitySuwon16419Republic of Korea Facultyof Science Universityof KragujevacP.O.Bor 6034000 KragujevacSerbia

The Merrifield–Simmons indexσis the total number of independent vertex sets(including the empty set)of the graph *** Wiener index W is the sum of distances in all unordered pairs of vertices of *** construct some new graphs satisfyingσ>W and W>σ,*** particular,infinite graphs satisfying W>σare invented with graphs with diameter 2 and infinite ones satisfyingσ>W are discovered with so-called universally diametrical graphs.

关键词： Merrifield–Simmons index Wiener index Cartesian product independence number Fibonacci number universally diametrical graph

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