Add to ORKGThe inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a crucial surgery method, we begin by proving the simpler related upper bounds (4(|V | − 1) − |E|)/3 and 4|V |2/3|E | on the diameter (for connected planar graphs), which are also tight.
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a ...
AbstractWe define a graph associated with a group G by letting nontrivial degrees be the vertices, a...
In graph theory, the degree diameter problem asks for the maximum number of vertices a graph with gi...
AbstractThe inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. ...
AbstractThe inverse degree r(G) of a finite graph G=(V,E) is defined as r(G)=∑v∈V1degv, where degv i...
AbstractThe inverse degree r(G) of a finite graph G=(V,E) is defined as r(G)=∑v∈V1degv. We prove tha...
Any connected plane nearest neighbor graph has diameter Ω(n^1/6). This bound generalizes to Ω(n^1/3d...
AbstractLet D be a strongly connected oriented graph, i.e., a digraph with no cycles of length 2, of...
AbstractWe offer the exact solution of the degree–diameter problem for planar graphs in the case of ...
We show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is eq...
The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree a...
The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree a...
AbstractIn this note, we use a technique introduced by Dankelmann and Entringer [P. Dankelmann, R.C....
The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree a...
AbstractWe prove that for every connected 4-colourable graph G of order n and minimum degree δ≥1, di...
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a ...
AbstractWe define a graph associated with a group G by letting nontrivial degrees be the vertices, a...
In graph theory, the degree diameter problem asks for the maximum number of vertices a graph with gi...
AbstractThe inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. ...
AbstractThe inverse degree r(G) of a finite graph G=(V,E) is defined as r(G)=∑v∈V1degv, where degv i...
AbstractThe inverse degree r(G) of a finite graph G=(V,E) is defined as r(G)=∑v∈V1degv. We prove tha...
Any connected plane nearest neighbor graph has diameter Ω(n^1/6). This bound generalizes to Ω(n^1/3d...
AbstractLet D be a strongly connected oriented graph, i.e., a digraph with no cycles of length 2, of...
AbstractWe offer the exact solution of the degree–diameter problem for planar graphs in the case of ...
We show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is eq...
The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree a...
The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree a...
AbstractIn this note, we use a technique introduced by Dankelmann and Entringer [P. Dankelmann, R.C....
The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree a...
AbstractWe prove that for every connected 4-colourable graph G of order n and minimum degree δ≥1, di...
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a ...
AbstractWe define a graph associated with a group G by letting nontrivial degrees be the vertices, a...
In graph theory, the degree diameter problem asks for the maximum number of vertices a graph with gi...