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A Characterization for 2-Self-Centered Graphs

Mohammad Hadi ShekarrizMadjid MirzavaziriKamyar Mirzavaziri — 2018

Discussiones Mathematicae Graph Theory

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...

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