Response to “Comment on ‘The single-wall carbon nanotube waveguides and excitation of their σ+π plasmons by an electron beam’ †[Phys. Plasmas 16, 054705 (2009)]
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We prove that every triangle-free planar graph with minimum degree 3 has radius at least 3; equivalently, no vertex neighborhood is a dominating set.
- ON THREE CONJECTURES INVOLVING THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF GRAPHS. Lihua Feng; Guihai Yu // Publications de l'Institut Mathematique;2009, Issue 99, p35
We study the signless Laplacian spectral radius of graphs and prove three conjectures of Cvetkovic, Rowlinson, and Simic [Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math., Nouv. S�r. 81(95) (2007), 11-27].
- ON THE STRUCTURE OF COMAXIMAL GRAPHS OF COMMUTATIVE RINGS WITH IDENTITY. Moconja, Slavko M.; Petrović, Zoran Z. // Bulletin of the Australian Mathematical Society;06/22/2010, Vol. 83 Issue 1, p11
In this paper we investigate the center, radius and girth of comaximal graphs of commutative rings. We also provide some counterexamples to the results concerning the relation between isomorphisms of comaximal graphs and the rings in question. In addition, we investigate the relation between the...
- The diameter of an interval graph is twice of its radius. Pramanik, Tarasankar; Mondal, Sukumar; Pal, Madhumangal // World Academy of Science, Engineering & Technology;Aug2011, Issue 56, p1363
In an interval graph G = (V,E) the distance between two vertices u, v is defined as the smallest number of edges in a path joining u and v. The eccentricity of a vertex v is the maximum among distances from all other vertices of V. The diameter (δ) and radius (Ï) of the graph G is...
- ON (k, l)-RADIUS OF RANDOM GRAPHS. Horváthová, M. // Acta Mathematica Universitatis Comenianae;2006, Vol. 75 Issue 2, p149
We introduce the concept of (k, l)-radius of a graph and prove that for any fixed pair k, l the (k, l)-radius is equal to 2(2k) - (2l) for almost all graphs. Since for k = 2 and l = 0 the (k, l)-radius is equal to the diameter, our result is a generalization of the known fact that almost all...
- On size, radius and minimum degree. Mukwembi, Simon // Discrete Mathematics & Theoretical Computer Science (DMTCS);2014, Vol. 16 Issue 1, p1
Let G be a finite connected graph. We give an asymptotically tight upper bound on the size of G in terms of order, radius and minimum degree. Our result is a strengthening of an old classical theorem of Vizing (1967) if minimum degree is prescribed.
- REMARKS ON A CONJECTURE ABOUT RANDIĆ INDEX AND GRAPH RADIUS. DEHGHAN-ZADEH, T.; HONGBO HUA; ASHRAFI, A. R.; HABIBI, N. // Miskolc Mathematical Notes;2013, Vol. 14 Issue 3, p845
Let G be a nontrivial connected graph. The radius r(G) of G is the minimum eccentricity among eccentricities of all vertices in G. The Randić index of G is defined as r(G) = ... and the Harmonic index is defined as H(G) = ... where dG(x) is the degree of the vertex x in G. In 1988,...
- Computing the maximal signless Laplacian index among graphs of prescribed order and diameter. Abreu, Nair; Lenes, Eber; Rojo, Oscar // Proyecciones - Journal of Mathematics;Dec2015, Vol. 34 Issue 4, p379
A bug Bugp,r1,r2 is a graph obtained from a complete graph Kp by deleting an edge uv and attaching the paths Pr1 and Pr2 by one of their end vertices at u and v, respectively. Let Q(G) be the signless Laplacian matrix of a graph G and q1(G) be the spectral radius of Q(G). It is known that the...
- The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter. Haixia Zhang // Journal of Applied Mathematics;2013, p1
We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d.
