Characterization Of Super-Radial Graphs

• Autorzy: K.M. Kathiresan , G. Marimuthu , C. Parameswaran
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

radius; diameter; super-radial graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 829-848

Daty

wydano

2014-11-01

otrzymano

2013-06-25

poprawiono

2013-10-28

zaakceptowano

2013-12-04

online

2014-11-15

Twórcy

autor

K.M. Kathiresan

• Center for Research and Post Graduate Studies in Mathematics Ayya Nadar Janaki Ammal College Sivakasi-626 124,Tamil Nadu, India

autor

G. Marimuthu

• Department of Mathematics The Madura College Madurai-625 011, Tamil Nadu, India

autor

C. Parameswaran

• Center for Research and Post Graduate Studies in Mathematics Ayya Nadar Janaki Ammal College Sivakasi-626 124,Tamil Nadu, India

Bibliografia

• [1] J. Akiyama, K. Ando and D. Avis, Eccentric graphs, Discrete Math. 56 (1985) 1-6. doi:10.1016/0012-365X(85)90188-8
• [2] R. Aravamuthan and B. Rajendran, Graph equations involving antipodal graphs, presented at the Seminar on Combinatorics and Applications held at ISI, Calcutta during 14-17 December (1982), 40-43.
• [3] R. Aravamuthan and B. Rajendran, On antipodal graphs, Discrete Math. 49 (1984) 193-195. doi:10.1016/0012-365X(84)90117-1
• [4] R. Aravamuthan and B. Rajendran, A note on antipodal graphs, Discrete Math. 58 (1986) 303-305. doi:10.1016/0012-365X(86)90148-2
• [5] F. Buckley and F. Harary, Distance in Graphs (Addition-Wesley, Reading, 1990).
• [6] F. Buckley, The eccentric digraphs of a graph, Congr. Numer. 149 (2001) 65-76.
• [7] E. Prisner, Graph Dynamics (Longman, London, 1995).
• [8] G. Johns and K. Sleno, Antipodal graphs and digraphs, Internat. J. Math. Soc. 16 (1993) 579-586. doi:10.1155/S0161171293000717
• [9] G. Johns, A simple proof of the characterization of antipodal graphs, Discrete Math. 128 (1994) 399-400. doi:10.1016/0012-365X(94)90131-7
• [10] Iqbalunnisa, T.N. Janakiraman and N. Srinivasan, On antipodal eccentric and supereccentric graph of a graph, J. Ramanujan Math. Soc. 4(2) (1989) 145-161.
• [11] J. Boland, F. Buckley and M. Miller, Eccentric digraphs, Discrete Math. 286 (2004) 25-29. doi:10.1016/j.disc.2003.11.041
• [12] J. Gimbert, M. Miller, F. Ruskey and J. Ryan, Iterations of eccentric digraphs, Bull.
• Inst. Combin. Appl. 45 (2005) 41-50.
• [13] J. Gimbert, N. Lopez, M. Miller and J. Ryan, Characterization of eccentric digraphs, Discrete Math. 306 (2006) 210-219. doi:10.1016/j.disc.2005.11.015
• [14] KM. Kathiresan and G. Marimuthu, A study on radial graphs, Ars Combin. 96 (2010) 353-360.
• [15] KM. Kathiresan and G. Marimuthu, Further results on radial graphs, Discuss. Math. Graph Theory 30 (2010) 75-83. doi:10.7151/dmgt.1477
• [16] KM. Kathiresan, G. Marimuthu and S. Arockiaraj, Dynamics of radial graphs, Bull. Inst. Combin. Appl. 57 (2009) 21-28.
• [17] KM. Kathiresan and R. Sumathi, Radial digraphs, Kragujevac J. Math. 34 (2010) 161-170.
• [18] KM. Kathiresan, S. Arockiaraj and C. Parameswaran, Characterization of supereccentric graphs, submitted.
• [19] M.I. Huilgol, S.A.S. Ulla and A.R. Sunilchandra, On eccentric digraphs of graphs, Appl. Math. 2 (2011) 705-710. doi:10.4236/am.2011.26093
• [20] N. López, A generalization of digraph operators related to distance properties in digraphs, Bulletin of the ICA 60 (2010) 49-61.
• [21] R.R. Singleton, There is no irregular Moore graph, Amer. Math. Monthly 75 (1968) 42-43. doi:10.2307/2315106
• [22] D.B. West, Introduction to Graph Theory (Prentice-Hall of India, New Delhi, 2003).
• [23] X. An and B. Wu, The Wiener index of the kth power of a graph, Appl. Math. Lett. 21 (2008) 436-440. doi:10.1016/j.aml.2007.03.025

Identyfikatory

DOI

10.7151/dmgt.1769