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arXiv · 1910.12110

A Characterization For 2-Self-Centered Graphs

Mohammad Hadi Shekarriz·Madjid Mirzavaziri·Kamyar Mirzavaziri
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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.

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Mohammad Hadi Shekarriz, Madjid Mirzavaziri, Kamyar Mirzavaziri. 2019-10-26. A Characterization For 2-Self-Centered Graphs. https://doi.org/10.7151/dmgt.1994

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