Discussiones Mathematicae Graph Theory, Volume (38), No (1), Year (2018-1) , Pages (27-37)

Title : ( A characterization for 2-self-centered graphs )

Authors: Mohammad Hadi Shekarriz , K. Mirzavaziri , Madjid Mirzavaziri ,

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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 intro- ducing specialized bi-independent covering (SBIC) and a structure named generalized complete bipartite graph (GCBG). Then, we complete charac- terization 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.


, self-centered graphs, specialized bi-independent covering (SBIC), generalized complete bipartite graphs (GCB).
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author = {Shekarriz, Mohammad Hadi and K. Mirzavaziri and Mirzavaziri, Madjid},
title = {A characterization for 2-self-centered graphs},
journal = {Discussiones Mathematicae Graph Theory},
year = {2018},
volume = {38},
number = {1},
month = {January},
issn = {1234-3099},
pages = {27--37},
numpages = {10},
keywords = {self-centered graphs; specialized bi-independent covering (SBIC); generalized complete bipartite graphs (GCB).},


%0 Journal Article
%T A characterization for 2-self-centered graphs
%A Shekarriz, Mohammad Hadi
%A K. Mirzavaziri
%A Mirzavaziri, Madjid
%J Discussiones Mathematicae Graph Theory
%@ 1234-3099
%D 2018