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Metric dimension and zero forcing number of two families of line graphs

Linda Eroh, Cong X. Kang, Eunjeong Yi (2014)

Mathematica Bohemica

Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that Z ( G ) ≤ 2 Z ( L ( G ) ) for a simple and connected graph G . Further,...

Metrically regular square of metrically regular bipartite graphs of diameter D = 7

Vladimír Vetchý (2018)

Archivum Mathematicum

The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only two tables of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter D = 7 (8 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter D < 7 see [8], [9] and [10].

Metrically regular square of metrically regular bipartite graphs of diameter D = 6

Vladimír Vetchý (1993)

Archivum Mathematicum

The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter D = 6 (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter D < 6 see [7] and [8].

Minimal c p rank.

Shaked-Monderer, Naomi (2001)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Kamal Lochan Patra, Binod Kumar Sahoo (2013)

Czechoslovak Mathematical Journal

In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on n vertices with girth g ( n , g being fixed), which graph minimizes the Laplacian spectral radius? Let U n , g be the lollipop graph obtained by appending a pendent vertex of a path on n - g ( n > ...

New bounds on the Laplacian spectral ratio of connected graphs

Zhen Lin, Min Cai, Jiajia Wang (2024)

Czechoslovak Mathematical Journal

Let G be a simple connected undirected graph. The Laplacian spectral ratio of G is defined as the quotient between the largest and second smallest Laplacian eigenvalues of G , which is an important parameter in graph theory and networks. We obtain some bounds of the Laplacian spectral ratio in terms of the number of the spanning trees and the sum of powers of the Laplacian eigenvalues. In addition, we study the extremal Laplacian spectral ratio among trees with n vertices, which improves some known...

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