Remarks on spectral radius and Laplacian eigenvalues of a graph

Bo Zhou; Han Hyuk Cho

Displaying similar documents to “Remarks on spectral radius and Laplacian eigenvalues of a graph”

Bounds on Laplacian eigenvalues related to total and signed domination of graphs

Wei Shi, Liying Kang, Suichao Wu (2010)

Czechoslovak Mathematical Journal

Similarity:

A total dominating set in a graph $G$ is a subset $X$ of $V (G)$ such that each vertex of $V (G)$ is adjacent to at least one vertex of $X$ . The total domination number of $G$ is the minimum cardinality of a total dominating set. A function $f : V (G) \to {- 1, 1}$ is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of an SDF is the sum of its function values over all vertices. The signed domination number of $G$ is the minimum weight of an SDF on $G$ . In...

Sharp upper bounds on the spectral radius of the Laplacian matrix of graphs.

Das, K.Ch. (2005)

Acta Mathematica Universitatis Comenianae. New Series

Similarity:

Near threshold graphs.

Kirkland, Steve (2009)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Kamal Lochan Patra, Binod Kumar Sahoo (2013)

Czechoslovak Mathematical Journal

Similarity:

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 $n - g$ $(n > g)$ vertices to a vertex of a cycle on $g \geq 3$ vertices. We prove that the graph $U_{n, g}$ uniquely minimizes the Laplacian spectral radius for $n \geq 2 g - 1$ when $g$ is even and for $n \geq 3 g - 1$ when $g$ is odd.

Graphs with the same peripheral and center eccentric vertices

Peter Kyš (2000)

Mathematica Bohemica

Similarity:

The eccentricity $e (v)$ of a vertex $v$ is the distance from $v$ to a vertex farthest from $v$ , and $u$ is an eccentric vertex for $v$ if its distance from $v$ is $d (u, v) = e (v)$ . A vertex of maximum eccentricity in a graph $G$ is called peripheral, and the set of all such vertices is the peripherian, denoted $P e r i G)$ . We use $C e p (G)$ to denote the set of eccentric vertices of vertices in $C (G)$ . A graph $G$ is called an S-graph if $C e p (G) = P e r i (G)$ . In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of...

Signed degree sets in signed graphs

Shariefuddin Pirzada, T. A. Naikoo, F. A. Dar (2007)

Czechoslovak Mathematical Journal

Similarity:

The set $D$ of distinct signed degrees of the vertices in a signed graph $G$ is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph.