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2016 | 36 | 1 | 127-140
Tytuł artykułu

On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G and H be two graphs. The join G ∨ H is the graph obtained by joining every vertex of G with every vertex of H. The corona G ○ H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the i-th vertex of G to every vertex in the i-th copy of H. The neighborhood corona G★H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. The edge corona G ◇ H is the graph obtained by taking one copy of G and |E(G)| copies of H and joining each terminal vertex of i-th edge of G to every vertex in the i-th copy of H. Let G1, G2, G3 and G4 be regular graphs with disjoint vertex sets. In this paper we compute the spectrum of (G1 ∨ G2) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ★ G4), (G1 ∨G2)∪(G1 ○G3), (G1 ∨G2)∪(G2 ○G3)∪(G1 ○G4), (G1 ∨G2)∪(G1 ◇G3), (G1 ∨ G2) ∪ (G2 ◇ G3) ∪ (G1 ◇ G4), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ◇ G4) and (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ◇ G4). As an application, we show that there exist some new pairs of equienergetic graphs on n vertices for all n ≥ 11.
Wydawca
Rocznik
Tom
36
Numer
1
Strony
127-140
Opis fizyczny
Daty
wydano
2016-02-01
otrzymano
2015-04-29
poprawiono
2015-05-25
zaakceptowano
2015-05-25
online
2016-01-19
Twórcy
  • Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysore – 570 006, India, c_adiga@hotmail.com
  • Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysore – 570 006, India, ranmsc08@yahoo.co.in
Bibliografia
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  • [7] S.-Y. Cui and G.-X. Tian, The spectrum and the signless Laplacian spectrum of coronae, Linear Algebra Appl. 437 (2012) 1692–1703. doi:10.1016/j.laa.2012.05.019[Crossref][WoS]
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  • [12] I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt. Forschungsz. Graz 103 (1978) 1–22.
  • [13] I. Gutman, The energy of a graph: old and new results, in: Algebraic Combinatorics and Applications, A. Betten, A. Kohnert, R. Laue and A. Wassermann (Ed(s)), (Berlin, Springer, 2000) 196–211.
  • [14] I. Gutman, Topology and stability of conjugated hydrocarbons. The dependence of total π-electron energy on molecular topology, J. Serb. Chem. Soc. 70 (2005) 441–456. doi:10.2298/JSC0503441G[Crossref]
  • [15] I. Gutman, D. Kiani, M. Mirzakhah and B. Zhou, On incidence energy of a graph, Linear Algebra Appl. 431 (2009) 1223–1233. doi:10.1016/j.laa.2009.04.019[WoS][Crossref]
  • [16] Y. Hou and W.-C. Shiu, The spectrum of the edge corona of two graphs, Electron. J. Linear Algebra 20 (2010) 586–594. doi:10.13001/1081-3810.1395[Crossref]
  • [17] G. Indulal, The spectrum of neighborhood corona of graphs, Kragujevac J. Math. 35 (2011) 493–500.
  • [18] G. Indulal and A. Vijayakumar, On a pair of equienergetic graphs, MATCH. Commun. Math. Comput. Chem. 55 (2006) 83–90.
  • [19] X. Li, Y. Shi and I. Gutman, Graph Energy (Springer, New York, 2012). doi:10.1007/978-1-4614-4220-2[Crossref]
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  • [23] X. Liu and S. Zhou, Spectra of the neighbourhood corona of two graphs, Linear Multilinear Algebra 62 (2014) 1205–1219. doi:10.1080/03081087.2013.816304[WoS][Crossref]
  • [24] C. McLeman and E. McNicholas, Spectra of coronae, Linear Algebra Appl. 435 (2011) 998–1007. doi:10.1016/j.laa.2011.02.007[WoS][Crossref]
  • [25] H.S. Ramane, I. Gutman, H.B. Walikar and S.B. Halkarni, Equienergetic complement graphs, Kragujevac J. Sci. 27 (2005) 67–74.
  • [26] H.S. Ramane and H.B. Walikar, Construction of equienergetic graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 203–210.
  • [27] D. Stevanović, Energy and NEPS of graphs, Linear Multilinear Algebra 53 (2005) 67–74. doi:10.1080/03081080410001714705[WoS][Crossref]
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  • [29] L. Xu and Y. Hou, Equienergetic bipartite graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 363–370.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1850
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