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

• Autorzy: Chandrashekar Adiga , B.R. Rakshith
• 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.

Słowa kluczowe

EN

spectrum; corona; neighbourhood corona; edge corona; energy of a graph; equienergetic graphs

Kategorie tematyczne

• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 1
• Strony: 127-140

Daty

wydano

2016-02-01

otrzymano

2015-04-29

poprawiono

2015-05-25

zaakceptowano

2015-05-25

online

2016-01-19

Twórcy

autor

Chandrashekar Adiga

• Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysore – 570 006, India

autor

B.R. Rakshith

• Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysore – 570 006, India

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1850