A Characterization for 2-Self-Centered Graphs

Mohammad Hadi Shekarriz, Madjid Mirzavaziri, and Kamyar Mirzavaziri. "A Characterization for 2-Self-Centered Graphs." Discussiones Mathematicae Graph Theory 38.1 (2018): 27-37. <http://eudml.org/doc/288522>.

@article{MohammadHadiShekarriz2018,
abstract = {A graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements. Then we split characterizing edge-minimal 2-self-centered graphs into two cases. First, we characterize edge-minimal 2-self-centered graphs without triangles by introducing specialized bi-independent covering (SBIC) and a structure named generalized complete bipartite graph (GCBG). Then, we complete characterization by characterizing edge-minimal 2-self-centered graphs with some triangles. Hence, the main characterization is done since a graph is 2-self-centered if and only if it is a spanning subgraph of some edge-maximal 2-self-centered graphs and, at the same time, it is a spanning supergraph of some edge-minimal 2-self-centered graphs.},
author = {Mohammad Hadi Shekarriz, Madjid Mirzavaziri, Kamyar Mirzavaziri},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {self-centered graphs; specialized bi-independent covering (SBIC); generalized complete bipartite graphs (GCB)},
language = {eng},
number = {1},
pages = {27-37},
title = {A Characterization for 2-Self-Centered Graphs},
url = {http://eudml.org/doc/288522},
volume = {38},
year = {2018},
}

TY - JOUR
AU - Mohammad Hadi Shekarriz
AU - Madjid Mirzavaziri
AU - Kamyar Mirzavaziri
TI - A Characterization for 2-Self-Centered Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2018
VL - 38
IS - 1
SP - 27
EP - 37
AB - A graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements. Then we split characterizing edge-minimal 2-self-centered graphs into two cases. First, we characterize edge-minimal 2-self-centered graphs without triangles by introducing specialized bi-independent covering (SBIC) and a structure named generalized complete bipartite graph (GCBG). Then, we complete characterization by characterizing edge-minimal 2-self-centered graphs with some triangles. Hence, the main characterization is done since a graph is 2-self-centered if and only if it is a spanning subgraph of some edge-maximal 2-self-centered graphs and, at the same time, it is a spanning supergraph of some edge-minimal 2-self-centered graphs.
LA - eng
KW - self-centered graphs; specialized bi-independent covering (SBIC); generalized complete bipartite graphs (GCB)
UR - http://eudml.org/doc/288522
ER -