Characterization Of Super-Radial Graphs

K.M. Kathiresan; G. Marimuthu; C. Parameswaran

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 4, page 829-848
  • ISSN: 2083-5892

Abstract

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In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R*(G) based on G has the vertex set as in G and two vertices u and v are adjacent in R*(G) if the distance between them in G is greater than or equal to d(G) − r(G) + 1 in G. If G is disconnected, then two vertices are adjacent in R*(G) if they belong to different components. A graph G is said to be a super-radial graph if it is a super-radial graph R*(H) of some graph H. The main objective of this paper is to solve the graph equation R*(H) = G for a given graph G.

How to cite

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K.M. Kathiresan, G. Marimuthu, and C. Parameswaran. "Characterization Of Super-Radial Graphs." Discussiones Mathematicae Graph Theory 34.4 (2014): 829-848. <http://eudml.org/doc/269820>.

@article{K2014,
abstract = {In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R*(G) based on G has the vertex set as in G and two vertices u and v are adjacent in R*(G) if the distance between them in G is greater than or equal to d(G) − r(G) + 1 in G. If G is disconnected, then two vertices are adjacent in R*(G) if they belong to different components. A graph G is said to be a super-radial graph if it is a super-radial graph R*(H) of some graph H. The main objective of this paper is to solve the graph equation R*(H) = G for a given graph G.},
author = {K.M. Kathiresan, G. Marimuthu, C. Parameswaran},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {radius; diameter; super-radial graph},
language = {eng},
number = {4},
pages = {829-848},
title = {Characterization Of Super-Radial Graphs},
url = {http://eudml.org/doc/269820},
volume = {34},
year = {2014},
}

TY - JOUR
AU - K.M. Kathiresan
AU - G. Marimuthu
AU - C. Parameswaran
TI - Characterization Of Super-Radial Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 4
SP - 829
EP - 848
AB - In a graph G, the distance d(u, v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius, r(G), of the graph and the maximum eccentricity is called the diameter, d(G), of the graph. The super-radial graph R*(G) based on G has the vertex set as in G and two vertices u and v are adjacent in R*(G) if the distance between them in G is greater than or equal to d(G) − r(G) + 1 in G. If G is disconnected, then two vertices are adjacent in R*(G) if they belong to different components. A graph G is said to be a super-radial graph if it is a super-radial graph R*(H) of some graph H. The main objective of this paper is to solve the graph equation R*(H) = G for a given graph G.
LA - eng
KW - radius; diameter; super-radial graph
UR - http://eudml.org/doc/269820
ER -

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