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http://dx.doi.org/10.14317/jami.2014.675

SOME NEW RESULTS ON IRREGULARITY OF GRAPHS  

Tavakoli, M. (Department of Mathematics, Ferdowsi University of Mashhad)
Rahbarnia, F. (Department of Mathematics, Ferdowsi University of Mashhad)
Ashra, A.R. (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan)
Publication Information
Journal of applied mathematics & informatics / v.32, no.5_6, 2014 , pp. 675-685 More about this Journal
Abstract
Suppose G is a simple graph. The irregularity of G, irr(G), is the summation of imb(e) over all edges $uv=e{\in}G$, where imb(e) = |deg(u)-deg(v)|. In this paper, we investigate the behavior of this graph parameter under some old and new graph operations.
Keywords
Graph operation; irregularity;
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1 F. Aurenhammer, J. Hagauer, W. Imrich, Cartesian graph factorization at logarithmic cost per edge, Comput. Complexity 2(4) (1992) 331-349.   DOI
2 H. Abdo, D. Dimitrov, The total irregularity of graphs under graph operations, to appear in Discussiones Mathematicae Graph Theory.
3 M.O. Albertson, The irregularity of a graph, Ars Combin. 46 (1997) 219-225.
4 A. Astaneh-Asl and G.H. Fath-Tabar, Computing the First and Third Zagreb Polynomials of Cartesian Product of Graphs, Iranian J. Math. Chem. 2 (2011), 73-78.
5 L. Barriere, F. Comellas, C. Daflo, M.A. Fiol, The hierarchical product of graphs, Discrete Appl. Math. 157 (2009) 36-48.   DOI   ScienceOn
6 L. Barriere, C. Daflo, M.A. Fiol, M. Mitjana,The generalized hierarchical product of graphs, Discrete Math. 309 (2009) 3871-3881.   DOI   ScienceOn
7 T. Doslic, Vertex-Weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), 66-80.
8 G.H. Fath-Tabar, Old and new Zagreb index, MATCH Commun. Math. Comput. Chem., 65 (2011), 79-84.
9 I. Gutman and N. Trinajstic, Graph theory and molecular orbitals,Total ${\pi}$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538.   DOI   ScienceOn
10 I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83-92.
11 I. Gutman, P. Hansen, H. Melot, Variable neighborhood search for extremal graphs. 10. Comparison of irregularity indices for chemical trees, J. Chem. Inf. Model. 45 (2005) 222-230.   DOI   ScienceOn
12 R. Hammack, W. Imrich and S. Klavzar, Handbook of Product Graphs, 2nd ed., Taylor & Francis Group, 2011.
13 P. Hansen, H. Melot, Variable neighborhood search for extremal graphs. 9. Bounding the irregularity of a graph, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 69 (2005) 253-264.
14 M.A. Henning, D. Rautenbach, On the irregularity of bipartite graphs, Discrete Math. 307 (2007) 1467-1472.   DOI   ScienceOn
15 S. Hossein-Zadeh, A. Hamzeh and A.R. Ashrafi, Extremal properties of Zagreb conindices and degree distance of graphs, Miskolc Math. Notes 11 (2) (2010), 129-137.   DOI
16 M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157 (2009) 804-811.   DOI   ScienceOn
17 W. Luo, B. Zhou, On the irregularity of trees and unicyclic graphs with given matching number, Util. Math. 83 (2010) 141-147.
18 D. Stevanovic, Hosoya polynomial of composite graphs, Discrete Math. 235 (2001) 237-244.   DOI   ScienceOn
19 M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A.R. Ashrafi, I. Gutman, Extremely irregular graphs, Kragujevac J. Math. 37 (1) (2013) 135-139.
20 W. Yan, B.-Y Yang and Y.-N Yeh, The behavior of Wiener indices and polynomials of graphs under five graph decorations, Appl. Math. Lett. 20 (2007) 290-295.   DOI   ScienceOn
21 B. Zhou, W. Luo, On irregularity of graphs, Ars Combin. 88 (2008) 55-64.
22 M.V. Diudea, B. Parv, Molecular Topology. 25. Hyper-Wiener index of dendrimers, MATCH Commun. Math. Comput. Chem. 32 (1995) 71-83.