# A Characterization for 2-Self-Centered Graphs

Mohammad Hadi Shekarriz; Madjid Mirzavaziri; Kamyar Mirzavaziri

Discussiones Mathematicae Graph Theory (2018)

- Volume: 38, Issue: 1, page 27-37
- ISSN: 2083-5892

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topMohammad 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 -

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