Studying the corona product of graphs under some graph invariants

Document Type: Research Paper

Authors

1 University of Mashhad

2 University of Kashan

Abstract

‎‎The corona product $G\circ H$ of two graphs $G$ and $H$ is‎ ‎obtained by taking one copy of $G$ and $|V(G)|$ copies of $H$;‎ ‎and by joining each vertex of the $i$-th copy of $H$ to the‎ ‎$i$-th vertex of $G$‎, ‎where $1 \leq i \leq |V(G)|$‎. ‎In this‎ ‎paper‎, ‎exact formulas for the eccentric distance sum and the edge‎ ‎revised Szeged indices of the corona product of graphs are‎ ‎presented‎. ‎We also study the conditions under which the corona‎ ‎product of  graphs produces a median graph‎.

Keywords

Main Subjects

References

H. Wiener (1947). Structural determination of paran boiling points. J. Am. Chem. Soc.. 69, 17-20
Y. N. Yeh and I. Gutman (1994). On the sum of all distances in composite graphs. Discrete Math.,. 135, 359-365
V. Sharma, R. Goswami and A. K. Madan (1997). Eccentric connectivity index: a novel highly discriminating topological descriptor for structure property and structure activity studies. J. Chem. Inf. Comput. Sci.. 37, 273-282
A. R. Ashra , T. Doslic and M. Saheli (2011). The eccentric connectivity index of TUC4C8(R) nanotubes. MATCH Commun. Math. Comput. Chem.. 65, 221-230
A. R. Ashra , M. Saheli and M. Ghorbani (2011). The eccentric connectivity index of nanotubes and nanotori. J. Comput. Appl. Math.. 235, 4561-4566
G. Yu, L. Feng and A. Ilic (2011). On the eccentric distance sum of trees and unicyclic graphs. J. Math. Anal. Appl.. 375, 99-107
B. Zhou and Z. Du (2010). On eccentric connectivity index. MATCH Commun. Math. Comput. Chem.. 63, 181-198
A. Ilic and I. Gutman (2011). Eccentric connectivity index of chemical trees. MATCH Commun. Math. Comput. Chem.. 65, 731-744
M. J. Morgan, S. Mukwembi and H. C. Swart (2011). On the eccentric connectivity index of a graph. Discrete Math.. 311, 1229-1234
S. Gupta, M. Singh and A. K. Madan (2002). Eccentric distance sum: A novel graph invariant for predicting biological and physical properties. J. Math. Anal. Appl.. 275, 386-401
I. Gutman (1994). A formula for the Wiener number of trees and its extension to graphs containing cycles. Graph Theory Notes New York. 27, 9-15
I. Gutman and A. R. Ashra (2008). The edge version of the Szeged index. Croat. Chem. Acta. 81, 263-266
T. Pisanski and M. Randic (2010). Use of the Szeged index and the revised Szeged index for measuring network bipartivity. Discrete Appl. Math.. 158, 1936-1944
M. Randic (2002). On generalization of Wiener index for cyclic structures. Acta Chim. Slov.. 49, 483-496
H. Youse -Azari, M. H. Khalifeh and A. R. Ashra (2011). Calculating the edge Wiener and edge Szeged indices of graphs. J. Comput. Appl. Math.. 235, 4866-4870
M. Aouchiche and P. Hansen (2010). on a conjecture about the Szeged index. European J. Combin.,. 31, 1662-1666
A. Ilic, S. Klavzar and M. Milanovic (2010). On distance-balanced graphs. European J. Combin.. 31, 733-737
M. Tavakoli, F. Rahbarnia and A. R. Ashra (2013). Further results on Distance-Balanced graphs. Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys.. 75 (1), 77-84
K. Handa (1999). Bipartite graphs with balanced (a; b)-partitions. Ars Combin.. 51, 113-119
J. Jerebic, S. Klavzar and D. F. Rall (2008). Distance-balanced graphs. Ann. Comb.. 12, 71-79
M. Tavakoli, H. Youse -Azari and A. R. Ashra (2012). Note on edge distance-balanced graphs. Trans. Comb.. 1 (1), 1-6
R. Hammack, W. Imrich and S. Klavzar (2011). Handbook of Product Graphs. 2^nd ed., Taylor & Francis Group,.
T. Doslic (2008). Vertex-Weighted Wiener polynomials for composite graphs. Ars Math. Contemp.. 1, 66-80
Transactions on Combinatorics

Volume 3, Issue 3
September 2014
Pages 43-49

Files

Share

How to cite

Statistics