Characterizing 2-distance graphs

Let X be a finite simple graph. The 2-distance graph D2(X) of X is the graph with the same vertex set as X and two vertices are adjacent if and only if their distance in X is exactly 2. A graph G is a 2-distance graph if there exists a graph X such that D2(X)≅G. In this paper, we give three characte...

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Main Authors:	Ching, Ramuel P, Garces, Ian June L
Format:	text
Published:	Archīum Ateneo 2019
Subjects:	Distance in graphs 2-distance graph complement of a graph cocktail party graph bipartite graph complete graph Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/52 https://www.worldscientific.com/doi/abs/10.1142/S1793557119500062
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Institution:	Ateneo De Manila University

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spelling	ph-ateneo-arc.mathematics-faculty-pubs-10512020-03-06T07:14:25Z Characterizing 2-distance graphs Ching, Ramuel P Garces, Ian June L Let X be a finite simple graph. The 2-distance graph D2(X) of X is the graph with the same vertex set as X and two vertices are adjacent if and only if their distance in X is exactly 2. A graph G is a 2-distance graph if there exists a graph X such that D2(X)≅G. In this paper, we give three characterizations of 2-distance graphs, and find all graphs X such that D2(X)≅kP2 or Km∪Kn, where k≥2 is an integer, P2 is the path of order 2, and Km is the complete graph of order m≥1. 2019-01-01T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/52 https://www.worldscientific.com/doi/abs/10.1142/S1793557119500062 Mathematics Faculty Publications Archīum Ateneo Distance in graphs 2-distance graph complement of a graph cocktail party graph bipartite graph complete graph Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
country	Philippines
collection	archium.Ateneo Institutional Repository
topic	Distance in graphs 2-distance graph complement of a graph cocktail party graph bipartite graph complete graph Mathematics
spellingShingle	Distance in graphs 2-distance graph complement of a graph cocktail party graph bipartite graph complete graph Mathematics Ching, Ramuel P Garces, Ian June L Characterizing 2-distance graphs
description	Let X be a finite simple graph. The 2-distance graph D2(X) of X is the graph with the same vertex set as X and two vertices are adjacent if and only if their distance in X is exactly 2. A graph G is a 2-distance graph if there exists a graph X such that D2(X)≅G. In this paper, we give three characterizations of 2-distance graphs, and find all graphs X such that D2(X)≅kP2 or Km∪Kn, where k≥2 is an integer, P2 is the path of order 2, and Km is the complete graph of order m≥1.
format	text
author	Ching, Ramuel P Garces, Ian June L
author_facet	Ching, Ramuel P Garces, Ian June L
author_sort	Ching, Ramuel P
title	Characterizing 2-distance graphs
title_short	Characterizing 2-distance graphs
title_full	Characterizing 2-distance graphs
title_fullStr	Characterizing 2-distance graphs
title_full_unstemmed	Characterizing 2-distance graphs
title_sort	characterizing 2-distance graphs
publisher	Archīum Ateneo
publishDate	2019
url	https://archium.ateneo.edu/mathematics-faculty-pubs/52 https://www.worldscientific.com/doi/abs/10.1142/S1793557119500062
_version_	1681506544091398144

Characterizing 2-distance graphs

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