January 2014
Miskolc Mathematical Notes;2014, Vol. 15 Issue 1, p97
Academic Journal
Let G be a connected graph with vertex set V(G). The degree Kirchhoff index of G is defined as S'(G) = Σ {u,υ}⊆V(G) d(u)d(υ)R(u,υ), where d(u) is the degree of vertex u, and R(u,υ) denotes the resistance distance between vertices u and υ. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result for the degree Kirchhoff index.


Related Articles

  • LAPLACIAN COEFFICIENTS OF UNICYCLIC GRAPHS WITH THE NUMBER OF LEAVES AND GIRTH. Jie Zhang; Xiao-Dong Zhang // Applicable Analysis & Discrete Mathematics;2014, Vol. 8 Issue 2, p330 

    Motivated by Ilić and Ilić's conjecture [A. ILIĆ, M. ILIĆ: Laplacian coefficients of trees with given number of leaves or vertices of degree two. Linear Algebra Appl., 431 (2009), 2195-2202.], we investigate properties of the minimal elements in the partial set (Ugn,ℓ,...

  • MORE ON THE NORMALIZED LAPLACIAN ESTRADA INDEX. Yilun Shang // Applicable Analysis & Discrete Mathematics;2014, Vol. 8 Issue 2, p346 

    Let G be a simple graph of order N. The normalized Laplacian Estrada index of G is defined as NEE(G) = ∑Ni=1eλi-1, where λ1, λ2 ⋯, λN the normalized Laplacian eigenvalues of G. In this paper, we give a tight lower bound for NEE of general graphs. We also calculate NEE for...

  • Quasilinear elliptic equations with Hardy terms and Hardy-Sobolev critical exponents: nontrivial solutions. Chen, Guanwei // Boundary Value Problems;9/23/2015, Vol. 2015 Issue 1, p1 

    In this paper, we obtain one positive solution and two nontrivial solutions of a quasilinear elliptic equation with p-Laplacian, Hardy term and Hardy-Sobolev critical exponent by using variational methods and some analysis techniques. In particular, our results extend some existing ones.

  • Positive Solutions for Discrete Sturm-Liouville-Like Four-Point p-Laplacian Boundary Value Problems. MENG ZHANG; SHURONG SUN; ZHENLAI HAN // Bulletin of the Malaysian Mathematical Sciences Society;2012, Vol. 35 Issue 2, p303 

    We consider the existence of positive solutions for a class of discrete second-order four-point boundary value problem with p-Laplacian. Using the well known Krasnosel'skii's fixed point theorem, some new existence criteria for positive solutions of the boundary value problem are presented.

  • The Existence of Three Positive Solutions to Integral Type BVPs for Second Order ODEs with One-Dimensional p-Laplacian. LIU, YUJI // Bulletin of the Malaysian Mathematical Sciences Society;2012, Vol. 35 Issue 2, p359 

    This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian {[p(t)Φ(x'(t))]'+f(t,x(t),(t))=0, tϵ(0,1), ø1(x(0))=∫01 g(s)ø1(s(s))ds, ø2(x'(1))=∫01h(s)ø2(x'(s)) ds. Sufficient...

  • Self-adapted Layer Contrast Enhancement Algorithm Based on Medical Image. HE Yi; ZHANG Ying-qian // Applied Mechanics & Materials;2014, Issue 556-562, p3416 

    The paper suggests a kind of self-adapted layer contrast enhancement algorithm for medical images, which, in reference to Laplacian pyramid function, could compose images, and enhance pixel contrast on each layer through F/E processing and use of self-adaptation Sigmoid function, and it uses...

  • A p-Laplace equation with nonlocal boundary condition in a perforated-like domain. Hailong Ye; Yuanyuan Ke // Bulletin of the Belgian Mathematical Society - Simon Stevin;2013, Vol. 20 Issue 5, p895 

    In this paper, we consider the radially symmetric solutions for p-Laplacian with nonlocal boundary condition in a perforated-like domain. We obtain the existence, the uniqueness and some other properties of the radially symmetric solution. The nonexistence of solution is also studied.

  • Laplacian Energy of Binary Labeled Graph. Bhat, Pradeep G.; D'Souza, Sabitha; Nayak, Swati S. // International Journal of Mathematical Combinatorics;Jun2015, Vol. 2, p106 

    Let G be a binary labeled graph and Al (G) = (lij) be its label adjacency matrix. For a vertex vi, we define label degree as ... . In this paper, we define label Laplacian energy LEl (G). It depends on the underlying graph G and labels of the vertices. We compute label Laplacian spectrum of...

  • On Coefficients of the Characteristic Polynomial of the Laplace Matrix of a Weighted Digraph and the All Minors Theorem. Buslov, V. // Journal of Mathematical Sciences;Feb2016, Vol. 212 Issue 6, p643 

    Let L be the Laplace matrix of a weighted digraph. The aim of the paper is to establish a simple way for computing any coefficient of the characteristic polynomial of L as a constant sign sum over the incoming spanning forests. The idea is to express L as the product of generalized (weighted)...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics