A Characterization For 2-Self-Centered Graphs
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 \emph{specialized bi-independent covering (SBIC)} and a structure named \emph{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
Cite
@article{arxiv.1910.12110,
title = {A Characterization For 2-Self-Centered Graphs},
author = {Mohammad Hadi Shekarriz and Madjid Mirzavaziri and Kamyar Mirzavaziri},
journal= {arXiv preprint arXiv:1910.12110},
year = {2019}
}