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2014 | 34 | 2 | 263-278
Tytuł artykułu

The irregularity of graphs under graph operations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑uv∈E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and sym- metric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the above mentioned operations
Wydawca
Rocznik
Tom
34
Numer
2
Strony
263-278
Opis fizyczny
Daty
wydano
2014-05-01
online
2014-04-12
Twórcy
autor
  • Darko Dimitrov Institut für Informatik, Freie Universität Berlin Takustraße 9, D–14195 Berlin, Germany
  • Institut für Informatik, Freie Universität Berlin Takustraße 9, D–14195 Berlin, Germany, darko@mi.fu-berlin.de
Bibliografia
  • [1] H. Abdo and D. Dimitrov, Total irregularity of a graph, (2012) a manuscript. arxiv.org/abs/1207.5267
  • [2] Y. Alavi, A. Boals, G. Chartrand, P. Erdös and O.R. Oellermann, k-path irregular graphs, Congr. Numer. 65 (1988) 201-210.
  • [3] Y. Alavi, G. Chartrand, F.R.K. Chung, P. Erdös, R.L. Graham and O.R. Oeller- mann, Highly irregular graphs, J. Graph Theory 11 (1987) 235-249. doi:10.1002/jgt.3190110214[Crossref]
  • [4] Y. Alavi, J. Liu and J. Wang, Highly irregular digraphs, Discrete Math. 111 (1993) 3-10. doi:10.1016/0012-365X(93)90134-F[Crossref]
  • [5] M.O. Albertson, The irregularity of a graph, Ars Combin. 46 (1997) 219-225.
  • [6] M.O. Albertson and D. Berman, Ramsey graphs without repeated degrees, Congr. Numer. 83 (1991) 91-96.
  • [7] F.K. Bell, A note on the irregularity of graphs, Linear Algebra Appl. 161 (1992) 45-54. doi:10.1016/0024-3795(92)90004-T[Crossref]
  • [8] F.K. Bell, On the maximal index of connected graphs, Linear Algebra Appl. 144 (1991) 135-151. doi:10.1016/0024-3795(91)90067-7[Crossref]
  • [9] G. Chartrand, P. Erd˝os and O.R. Oellermann, How to define an irregular graph, College Math. J. 19 (1988) 36-42. doi:10.2307/2686701[Crossref]
  • [10] G. Chartrand, K.S. Holbert, O.R. Oellermann and H.C. Swart, F-degrees in graphs, Ars Combin. 24 (1987) 133-148.
  • [11] G. Chen, P. Erd˝os, C. Rousseau and R. Schelp, Ramsey problems involving degrees in edge-colored complete graphs of vertices belonging to monochromatic subgraphs, European J. Combin. 14 (1993) 183-189. doi:10.1006/eujc.1993.1023[Crossref]
  • [12] L. Collatz and U. Sinogowitz, Spektren endlicher Graphen, Abh. Math. Semin. Univ. Hamburg 21 (1957) 63-77. doi:10.1007/BF02941924[Crossref]
  • [13] D. Cvetkovi´c and P. Rowlinson, On connected graphs with maximal index , Publica- tions de l’Institut Mathematique Beograd 44 (1988) 29-34.
  • [14] K.C. Das and I. Gutman, Some properties of the second Zagreb index , MATCH Commun. Math. Comput. Chem. 52 (2004) 103-112.
  • [15] T. Došli´c, B. Furtula, A. Graovac, I. Gutman, S. Moradi and Z. Yarahmadi, On vertex degree based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66 (2011) 613-626.
  • [16] G.H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 65 (2011) 79-84.
  • [17] I. Gutman and K.C. Das, The first Zagreb index 30 years after , MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92.
  • [18] I. Gutman, P. Hansen and H. M´elot, Variable neighborhood search for extremal graphs. 10. Comparison of irregularity indices for chemical trees, J. Chem. Inf. Model. 45 (2005) 222-230. doi:10.1021/ci0342775[Crossref]
  • [19] R. Hammack, W. Imrich and S. Klavˇzar, Handbook of Product Graphs (CRC Press, Boca Raton, FL, 2011).
  • [20] P. Hansen and H.M´elot, Variable neighborhood search for extremal graphs. 9. Bounding the irregularity of a graph, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 69 (2005) 253-264.
  • [21] M.A. Henning and D. Rautenbach, On the irregularity of bipartite graphs, Discrete Math. 307 (2007) 1467-1472.[WoS]
  • [22] D.E. Jackson and R. Entringer, Totally segregated graphs, Congr. Numer. 55 (1986) 159-165.
  • [23] D.J. Miller, The categorical product of graphs, Canad. J. Math. 20 (1968) 1511-1521. doi:10.4153/CJM-1968-151-x[Crossref]
  • [24] S. Nikoli´c, G. Kovaˇcevi´c, A. Miliˇcevi´c and N. Trinajsti´c, The Zagreb indices 30 years after , Croat. Chem. Acta 76 (2003) 113-124.
  • [25] N. Trinajsti´c, S. Nikoli´c, A. Miliˇcevi´c and I. Gutman, On Zagreb indices, Kem. Ind. 59 (2010) 577-589.
  • [26] P.M. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc. 13 (1962) 47-52. doi:10.4153/CJM-1968-151-x[Crossref]
  • [27] V. Yegnanarayanan, P.R. Thiripurasundari and T. Padmavathy, On some graph operations and related applications, Electron. Notes Discrete Math. 33 (2009) 123-130. doi:10.1016/j.endm.2009.03.018[Crossref]
  • [28] B. Zhou, Remarks on Zagreb indices, MATCH Commun. Math. Comput. Chem. 57 (2007) 591-596.
  • [29] B. Zhou and I. Gutman, Further properties of Zagreb indices, MATCH Commun. Math. Comput. Chem 54 (2005) 233-239.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1733
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