Add to ORKGWe find an upper bound on the algebraic connectivity of graphs of various genus. We begin by showing that for fixed k ⩾ 1, the graph of genus k of largest algebraic connectivity is a complete graph. We then find an upper bound for noncomplete graphs of a fixed genus k ⩾ 1 and we determine the values of k for which the upper bound can be attained. Finally, we find the upper bound of the algebraic connectivity of planar graphs (graphs of genus zero) and determine precisely which graphs attain this upper bound
AbstractLower bounds on the cardinality of the maximum matchings of graphs are established in terms ...
AbstractIt is shown that ⌈β(G)/3⌉ is the tight lower bound on the maximum genus γM(G) of 2-edge-conn...
The $d$-dimensional algebraic connectivity $a_d(G)$ of a graph $G=(V,E)$, introduced by Jord\'an and...
AbstractWe find an upper bound on the algebraic connectivity of graphs of various genus. We begin by...
AbstractWe find an upper bound on the algebraic connectivity of graphs of various genus. We begin by...
The structure of connected graphs of given size and order that have minimal algebraic connectivity i...
Let G be an undirected unweighted graph on n vertices and let L be its Laplacian matrix. It is known...
It is well known that the algebraic connectivity of a graph is the second small eigenvalue of its La...
AbstractLet G be a connected graph of order n. The algebraic connectivity of G is the second smalles...
AbstractThis paper is a survey of the second smallest eigenvalue of the Laplacian of a graph G, best...
AbstractIn this paper, the lower bounds of maximum genera of simplicial graphs under the constraints...
AbstractLet c(G) denote the number of components in a graph G. It is shown that if G has genus γ and...
AbstractThis paper introduces the connection-graph-stability method and uses it to establish a new l...
In this paper, we determine upper bounds on the algebraic connectivity, denoted as a(G), of maximal ...
AbstractGiven an undirected graph G=(V,E) and a nonempty subset X⊆V, the edge density of X is given ...
AbstractLower bounds on the cardinality of the maximum matchings of graphs are established in terms ...
AbstractIt is shown that ⌈β(G)/3⌉ is the tight lower bound on the maximum genus γM(G) of 2-edge-conn...
The $d$-dimensional algebraic connectivity $a_d(G)$ of a graph $G=(V,E)$, introduced by Jord\'an and...
AbstractWe find an upper bound on the algebraic connectivity of graphs of various genus. We begin by...
AbstractWe find an upper bound on the algebraic connectivity of graphs of various genus. We begin by...
The structure of connected graphs of given size and order that have minimal algebraic connectivity i...
Let G be an undirected unweighted graph on n vertices and let L be its Laplacian matrix. It is known...
It is well known that the algebraic connectivity of a graph is the second small eigenvalue of its La...
AbstractLet G be a connected graph of order n. The algebraic connectivity of G is the second smalles...
AbstractThis paper is a survey of the second smallest eigenvalue of the Laplacian of a graph G, best...
AbstractIn this paper, the lower bounds of maximum genera of simplicial graphs under the constraints...
AbstractLet c(G) denote the number of components in a graph G. It is shown that if G has genus γ and...
AbstractThis paper introduces the connection-graph-stability method and uses it to establish a new l...
In this paper, we determine upper bounds on the algebraic connectivity, denoted as a(G), of maximal ...
AbstractGiven an undirected graph G=(V,E) and a nonempty subset X⊆V, the edge density of X is given ...
AbstractLower bounds on the cardinality of the maximum matchings of graphs are established in terms ...
AbstractIt is shown that ⌈β(G)/3⌉ is the tight lower bound on the maximum genus γM(G) of 2-edge-conn...
The $d$-dimensional algebraic connectivity $a_d(G)$ of a graph $G=(V,E)$, introduced by Jord\'an and...