Results 11 to 20 of about 1,099 (125)
An O(mn2) Algorithm for Computing the Strong Geodetic Number in Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G = (V (G), E(G)) be a graph and S be a subset of vertices of G. Let us denote by γ[u, v] a geodesic between u and v. Let Γ(S) = {γ[vi, vj] | vi, vj ∈ S} be a set of exactly |S|(|S|−1)/2 geodesics, one for each pair of distinct vertices in S.
Mezzini Mauro
doaj +1 more source
Longer Cycles in Essentially 4-Connected Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 A planar 3-connected graph G is called essentially 4-connected if, for every 3-separator S, at least one of the two components of G − S is an isolated vertex.
Fabrici Igor +3 more
doaj +1 more source
, 2011 We investigate Legendrian graphs in .R 3 ; std/. We extend the Thurston‐Bennequin number and the rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with tbD 1 and rotD 0 if and ...
Danielle O'Donnol, Elena Pavelescu
semanticscholar +1 more source
International Journal of Apllied Mathematics, 2018 The degree of an edge uv is defined as the number of edges incident on vertices u and v other than itself. The Platt number of a graph is the sum of degrees of all its edges. In this paper, the concept of degree of an edge is analysed in social networks.
M. Belavadi, T. A. Mangam
semanticscholar +1 more source
Untwisting 3‐strand torus knots
Bulletin of the London Mathematical Society, Volume 52, Issue 3, Page 429-436, June 2020., 2020 Abstract We prove that the signature bound for the topological 4‐genus of 3‐strand torus knots is sharp, using McCoy's twisting method. We also show that the bound is off by at most 1 for 4‐strand and 6‐strand torus knots, and improve the upper bound on the asymptotic ratio between the topological 4‐genus and the Seifert genus of torus knots from 2/3 ...
S. Baader, I. Banfield, L. Lewark
wiley +1 more source
Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
doaj +1 more source
Long-Scale Ollivier Ricci Curvature of Graphs
Analysis and Geometry in Metric Spaces, 2019 We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and piecewise linear with at most 3 linear parts.
Cushing D., Kamtue S.
doaj +1 more source
A simple and elementary proof of Whitney's unique embedding theorem
, 2020 In this note we give a short and elementary proof of a more general version of Whitney's theorem that 3-connected planar graphs have a unique embedding in the plane.
Brinkmann, Gunnar
core +1 more source
Additive List Coloring of Planar Graphs with Given Girth
Discussiones Mathematicae Graph Theory, 2020 An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such that two adjacent vertices have distinct sums of labels on their neighbors.
Brandt Axel +2 more
doaj +1 more source
Non-1-Planarity of Lexicographic Products of Graphs
Discussiones Mathematicae Graph Theory, 2021 In this paper, we show the non-1-planarity of the lexicographic product of a theta graph and K2. This result completes the proof of the conjecture that a graph G ◦ K2 is 1-planar if and only if G has no edge belonging to two cycles.
Matsumoto Naoki, Suzuki Yusuke
doaj +1 more source