scholarly journals Dominating sets inducing large components in maximal outerplanar graphs

2017 ◽  
Vol 88 (2) ◽  
pp. 356-370
Author(s):  
José D. Alvarado ◽  
Simone Dantas ◽  
Dieter Rautenbach
Keyword(s):  
Dominating Sets ◽  
Outerplanar Graphs ◽  
Maximal Outerplanar Graphs

Total Dominating Sets in Maximal Outerplanar Graphs

2017 ◽  
Vol 33 (4) ◽  
pp. 991-998 ◽  
Author(s):  
Magdalena Lemańska ◽  
Rita Zuazua ◽  
Paweł Żyliński
Keyword(s):  
Dominating Sets ◽  
Outerplanar Graphs ◽  
Maximal Outerplanar Graphs

scholarly journals Combinatorial bounds on connectivity for dominating sets in maximal outerplanar graphs

2016 ◽  
Vol 54 ◽  
pp. 109-114 ◽  
Author(s):  
Santiago Canales ◽  
Irene Castro ◽  
Gregorio Hernández ◽  
Mafalda Martins
Keyword(s):  
Dominating Sets ◽  
Outerplanar Graphs ◽  
Maximal Outerplanar Graphs

scholarly journals On dominating sets of maximal outerplanar graphs

2013 ◽  
Vol 161 (3) ◽  
pp. 330-335 ◽  
Author(s):  
C.N. Campos ◽  
Y. Wakabayashi
Keyword(s):  
Dominating Sets ◽  
Outerplanar Graphs ◽  
Maximal Outerplanar Graphs

Convex dominating sets in maximal outerplanar graphs

2019 ◽  
Vol 265 ◽  
pp. 142-157 ◽  
Author(s):  
Magdalena Lemańska ◽  
Eduardo Rivera-Campo ◽  
Radosław Ziemann ◽  
Rita Zuazua ◽  
Paweł Żyliński
Keyword(s):  
Dominating Sets ◽  
Outerplanar Graphs ◽  
Maximal Outerplanar Graphs

scholarly journals An efficientg-centroid location algorithm for cographs

2005 ◽  
Vol 2005 (9) ◽  
pp. 1405-1413 ◽  
Author(s):  
V. Prakash
Keyword(s):  
Location Problem ◽  
Maximum Clique ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Outerplanar Graphs ◽  
Arbitrary Graph ◽  
Maximal Outerplanar Graphs ◽  
Split Graphs ◽  
Location Algorithm ◽  
Centroid Location

In 1998, Pandu Rangan et al. Proved that locating theg-centroid for an arbitrary graph is𝒩𝒫-hard by reducing the problem of finding the maximum clique size of a graph to theg-centroid location problem. They have also given an efficient polynomial time algorithm for locating theg-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present anO(nm)time algorithm for locating theg-centroid for cographs, wherenis the number of vertices andmis the number of edges of the graph.

scholarly journals Some New Classes of Open Distance-Pattern Uniform Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Bibin K. Jose
Keyword(s):  
Nonempty Subset ◽  
Chordal Graphs ◽  
Outerplanar Graph ◽  
Outerplanar Graphs ◽  
Induced Subgraphs ◽  
Minimum Cardinality ◽  
Maximal Outerplanar Graphs ◽  
Split Graphs ◽  
Strongly Chordal Graphs

Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern. The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). Given some property P, we establish characterization of odpu-graph with property P. In this paper, we characterize odpu-chordal graphs, and thereby characterize interval graphs, split graphs, strongly chordal graphs, maximal outerplanar graphs, and ptolemaic graphs that are odpu-graphs. We also characterize odpu-self-complementary graphs, odpu-distance-hereditary graphs, and odpu-cographs. We prove that the odpu-number of cographs is even and establish that any graph G can be embedded into a self-complementary odpu-graph H, such that G and G¯ are induced subgraphs of H. We also prove that the odpu-number of a maximal outerplanar graph is either 2 or 5.

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