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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2016 | 36 | 1 | 127-140

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

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.

EN

127-140

wydano
2016-02-01
otrzymano
2015-04-29
poprawiono
2015-05-25
zaakceptowano
2015-05-25
online
2016-01-19

### Twórcy

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

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