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| 1 | On a Novel Eccentricity-based Invariant of a Graph显示文摘In this paper,for the purpose of measuring the non-self-centrality extent of non-selfcentered graphs,a novel eccentricity-based invariant,named as non-self-centrality number(NSC number for short),of a graph G is defined as follows:N(G)=∑v_i,v_j∈V(G)|e_i-e_j| where the summation goes over all the unordered pairs of vertices in G and e_i is the eccentricity of vertex v_i in G,whereas the invariant will be called third Zagreb eccentricity index if the summation only goes over the adjacent vertex pairs of graph G.In this paper,we determine the lower and upper bounds on N(G) and characterize the corresponding graphs at which the lower and upper bounds are attained.Finally we propose some attractive research topics for this new invariant of graphs. | Ke Xiang XU Kinkar Ch.DAS Ayse Dilek MADEN | 2016 | Acta Mathematica Sinica,English Series2016，32，12： | 2 |
| 2 | Some new bounds on the spectral radius of graphs显示文摘 | Kinkar Ch. Das Pawan Kumar | 2003 | Discrete Mathematics2003，，： | 1 |
| 3 | Extremal unicyclic and bicyclic graphs with respect to Harary index显示文摘 | Xu K Das Ch Kinkar | 2013 | Asian Academy of Manage- ment Journal of accounting : Finance2013，9，2： | 1 |
| 4 | A sharp upper bound on the spectral radius of weighted graphs显示文摘 | Kinkar Ch. Das R.B. Bapat | 2007 | Discrete Mathematics2007，，15： | 1 |
| 5 | Zagreb indices of graphs显示文摘第一萨格勒布索引 M <潜水艇class=“ a-plus-plus ”> 1 (G)等于顶点的度的广场的和,并且第二萨格勒布索引 M <潜水艇class=“ a-plus-plus ”> 2 (G)等于一些内在的分子的图 G 的邻近的顶点的度的产品的和。在这份报纸,我们在第一萨格勒布索引 M 上获得更低、上面的界限 < 潜水艇 class= “ a-plus-plus ” > G 的 1 (G) 以顶点(n) 的数字,边(m) 的数字,最大的顶点度() ,并且最小的顶点度() 。用这结果,我们在 M 上发现更低、上面的界限 < 潜水艇 class= “ a-plus-plus ” > 2 (G) 。另外,我们 \ 上的现在的更低、上面的界限(M_2 (G)+ M_2 (\bar G )\) 以 n, m,,并且,,,并且,在 \(\bar G\) 表示 G 的补充的地方。而且,我们在第一萨格勒布 coindex \(\bar M_1 (G)\) 和第二萨格勒布 coindex \(\bar M_2 (G)\) 上决定界限。最后,我们给在第一个萨格勒布索引和图 G 的第二个萨格勒布索引之间的一种关系。 | Kinkar Ch. DAS Kexiang XU Junki NAM | 2015 | Frontiers of Mathematics in China2015，10，3： | 1 |
| 6 | On conjectures involving second largest signless Laplacian eigenvalue of graphs 显示文摘 | Kinkar C D | 2010 | Linear Algebra and Its Applications2010，432，： | 1 |
| 7 | Atom-bond connectivity index of graphs显示文摘 | Kinkar C D | 2010 | Discrete Applied Mathematics2010，158，11： | 1 |
| 8 | Sharp upper bounds on the spectral radius of the signless Laplacian matrix of a graph显示文摘 | A Dilek (GtingSr) Maden KINKAR Ch Das A Sinan Cevik | 2015 | Applied Mathematics and Computation2015，，219： | 1 |
| 9 | Das, Some new bounds on the spectral radius of graphs显示文摘 | Kinkar Ch | 2004 | Discrete Mathematics2004，，281： | 1 |
| 10 | Highly rapid and direct synthesis of diaryl sulfoxides 显示文摘 | B P Bandgar S N Kinkar V T Kamble | 2003 | Letter2003，13，： | 1 |
| 11 | Proof of conjecture involving the second largest signless Laplacian eigenvalue and the index of graphs 显示文摘 | KINKAR C D | 2001 | Linear Algebra and its Application2001，435，： | 1 |
| 12 | The Laplacian spectrum of a graph显示文摘 | Kinkar C D | | 0，，5： | 1 |
| 13 | A characterization on graphs which achieve the upper bound for the largest Laplacian eigenvalue of graphs显示文摘 | Kinkar Ch. Das | 2003 | Linear Algebra and Its Applications2003，，： | 1 |
| 14 | Comparison between Merrifield–Simmons Index and Wiener Index of Graphs显示文摘The Merrifield–Simmons indexσis the total number of independent vertex sets(including the empty set)of the graph G.The Wiener index W is the sum of distances in all unordered pairs of vertices of G.We construct some new graphs satisfyingσ>W and W>σ,respectively.In 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. | Ke Xiang XU Kinkar Chandra DAS Ivan GUTMAN Meng Lu WANG | 2022 | Acta Mathematica Sinica,English Series2022，38，12： | 0 |
| 15 | Distance signless Laplacian eigenvalues of graphs显示文摘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 vertices.Let 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 G.In 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 possible.We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs.Moreover,we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees,and characterize extremal graphs. | Kinkar Chandra DAS Huiqiu LIN Jiming GUO | 2019 | Frontiers of Mathematics in China2019，14，4： | 0 |
| 16 | Comparison and Extremal Results on Three Eccentricity-based Invariants of Graphs显示文摘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 G.The eccentric complexity C(ec)(G)of G is the number of different eccentricities of vertices in G.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. | Ke Xiang XU Kinkar Chandra DAS Xiao Qian GU | 2020 | Acta Mathematica Sinica,English Series2020，36，1： | 0 |
| 17 | Sum-connectivity index of a graph显示文摘让 G 是一张简单的连接的图,并且让 d i 是它的 i-th 顶点的度。图 G 的和连接索引被定义为 \(\chi (G)=\sum\nolimits_{ v_i v_j \in E (G)}{(d_i + d_j )^{- 1/2 }}\) 。我们在把一个边插入到一张图的(G) 上讨论效果。而且,我们获得在和连接之间的关系索引和 Randi 索引。 | Kinkar Ch. DAS Sumana DAS Bo ZHOU | 2016 | Frontiers of Mathematics in China2016，11，1： | 0 |
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