Geodesic
A Characterization for 2-Self-Centered Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 27-37

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: self-centered graphs, specialized bi-independent covering (SBIC), generalized complete bipartite graphs (GCB) 
@article{DMGT_2018_38_1_a1,
     author = {Shekarriz, Mohammad Hadi and Mirzavaziri, Madjid and Mirzavaziri, Kamyar},
     title = {A {Characterization} for {2-Self-Centered} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {27--37},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a1/}
}
TY  - JOUR
AU  - Shekarriz, Mohammad Hadi
AU  - Mirzavaziri, Madjid
AU  - Mirzavaziri, Kamyar
TI  - A Characterization for 2-Self-Centered Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2018
SP  - 27
EP  - 37
VL  - 38
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a1/
LA  - en
ID  - DMGT_2018_38_1_a1
ER  - 
%0 Journal Article
%A Shekarriz, Mohammad Hadi
%A Mirzavaziri, Madjid
%A Mirzavaziri, Kamyar
%T A Characterization for 2-Self-Centered Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2018
%P 27-37
%V 38
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a1/
%G en
%F DMGT_2018_38_1_a1
Shekarriz, Mohammad Hadi; Mirzavaziri, Madjid; Mirzavaziri, Kamyar. A Characterization for 2-Self-Centered Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 27-37. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a1/