Results 41 to 50 of about 213,970 (327)

Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants

Molecules, 2023
A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices.
Zheng-Qing Chu, Haidar Ali, Didar Abdulkhaleq Ali, Muhammad Nadeem, Syed Ajaz K. Kirmani, Parvez Ali   +5 more
doaj   +1 more source

Total Coloring of Claw-Free Planar Graphs

Discussiones Mathematicae Graph Theory, 2022
A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let Δ(G) be the maximum degree of G.
Liang Zuosong
doaj   +1 more source

Star edge coloring of $ K_{2, t} $-free planar graphs

AIMS Mathematics, 2023
The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges.
Yunfeng Tang , Huixin Yin , Miaomiao Han
doaj   +1 more source

Contact Representations of Graphs in 3D

, 2015
We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there
A Bezdek, B Mohar, C Thomassen, D Bremner, D Gonçalves, E Andreev, G Brinkmann, G Ringel, H Fraysseix de, H Schumacher, I Fabrici, J Czyzowicz, M Badent, N Bonichon, O Bernardi, P Hliněný, S Felsner, Y Suzuki   +17 more
core   +1 more source

An algorithm of graph planarity testing and cross minimization [PDF]

Computer Science Journal of Moldova, 2007
This paper presents an overview on one compartment from the graph theory, called graph planarity testing. It covers the fundamental concepts and important work in this area.
Vitalie Cotelea, Stela Pripa
doaj  

From light edges to strong edge-colouring of 1-planar graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail, François Dross, Hervé Hocquard, Eric Sopena   +3 more
doaj   +1 more source

Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends

, 2018
We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively.
C Bachmaier, D Harel, FJ Brandenburg, G Liotta, G Ringel, H Fraysseix de, H Purchase, JE Hopcroft, M Chrobak, MA Bekos, P Eades, SG Kobourov, W Didimo, W Huang   +13 more
core   +1 more source

Computing Planarity in Computable Planar Graphs

Graphs and Combinatorics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oscar Levin, Taylor McMillan
openaire   +2 more sources

Recognizing and Drawing IC-planar Graphs

, 2015
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs.
C Auer, C Auer, C Binucci, C Thomassen, D Král, E Ackerman, E Giacomo Di, E Giacomo Di, E Giacomo Di, EN Argyriou, FJ Brandenburg, H Fraysseix de, J Fox, J Pach, M Chrobak, MA Bekos, MJ Alam, MR Garey, O Cheong, OV Borodin, P Eades, S Hong, S-H Hong, VP Korzhik, W Didimo, W Didimo, X Zhang, X Zhang   +27 more
core   +1 more source

On the minimum size of maximal IC-plane graphs

AIMS Mathematics
A graph is IC-planar if it admits a drawing with at most one crossing per edge so that each vertex is incident to at most one crossing edge, and an IC-plane graph means such a drawing of an IC-planar graph.
Rui Xu
doaj   +1 more source