Results 11 to 20 of about 16,950 (147)

Symmetry breaking in planar and maximal outerplanar graphs [PDF]

Discrete Mathematics, Algorithms and Applications, 2018
The distinguishing number (index) [Formula: see text] ([Formula: see text]) of a graph [Formula: see text] is the least integer [Formula: see text] such that [Formula: see text] has a vertex (edge) labeling with [Formula: see text] labels that is ...
S. Alikhani, S. Soltani
semanticscholar   +5 more sources

Fuzzy Outerplanar Graphs and Its Applications

International Journal of Computational Intelligence Systems
The concept of a crisp graph is essential in the study of outerplanar graphs because outerplanar graphs are a unique type of planar graphs containing special characteristics. One of the core concepts of crisp graphs, the notion of a subgraph, is utilized
Deivanai Jaisankar, Sujatha Ramalingam, Nagarajan Deivanayagampillai, Tadesse Walelign   +3 more
doaj   +2 more sources

Disjunctive domination in maximal outerplanar graphs

arXiv.org
A disjunctive dominating set of a graph $G$ is a set $D \subseteq V(G)$ such that every vertex in $V(G)\setminus D$ has a neighbor in $D$ or has at least two vertices in $D$ at distance $2$ from it.
Michael A. Henning, P. Maniya, D. Pradhan   +2 more
semanticscholar   +3 more sources

Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs [PDF]

Australasian Journal of Combinatorics, 2011
Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices,
Laskar, R.C. (R.C.), Mulder, H.M. (Martyn), Novick, B. (Beth)   +2 more
core   +6 more sources

Optimal maximal graphs [PDF]

Transactions on Combinatorics, 2022
An optimal labeling of a graph with $n$ vertices and $m$ edges is an injective assignment of the first $n$ nonnegative integers to the vertices‎, ‎that induces‎, ‎for each edge‎, ‎a weight given by the sum of the labels of its end-vertices with the ...
Christian Barrientos, Maged Youssef
doaj   +1 more source

Maximally Expressive GNNs for Outerplanar Graphs

Journal of Machine Learning Research, 2023
Most pharmaceutical molecules can be represented as outerplanar graphs. We propose a graph transformation that makes the Weisfeiler-Leman (WL) test and message passing graph neural networks maximally expressive on outerplanar graphs. While existing research predominantly focuses on enhancing expressivity of graph neural networks beyond the WL test on ...
Bause, Franka, Jogl, Fabian, Welke, Pascal, Thiessen, Maximilian   +3 more
openaire   +3 more sources

Monitoring maximal outerplanar graphs [PDF]

Electronic Notes in Discrete Mathematics, 2014
In this paper we define a new concept of monitoring the elements of triangulation graphs by faces. Furthermore, we analyze this, and other monitoring concepts (by vertices and by edges), from a combinatorial point of view, on maximal outerplanar graphs.
Hernández Peñalver, Gregorio, Martins, Ana Mafalda   +1 more
openaire   +3 more sources

Linear Algorithms for Isomorphism of Maximal Outerplanar Graphs

Journal of the ACM, 1979
Terry Beyer, W. Jones, S. M. Hedetniemi
semanticscholar   +2 more sources

On the planarity of line Mycielskian graph of a graph

Ratio Mathematica, 2020
The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤  i ≤  q and e, then for 1 ≤  i ≤  q , joining ei' to the neighbours of ei  and  to e.
Keerthi G. Mirajkar, Anuradha V Deshpande   +1 more
doaj   +1 more source

A note on the double domination number in maximal outerplanar and planar graphs

RAIRO Oper. Res., 2022
In a graph, a vertex dominates itself and its neighbors. A subset S of vertices of a graph G is a double dominating set of G if S dominates every vertex of G at least twice.
Noor A'lawiah Abd Aziz, N. J. Rad, H. Kamarulhaili   +2 more
semanticscholar   +1 more source