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.
@article{bwmeta1.element.doi-10_7151_dmgt_1850,
author = {Chandrashekar Adiga and B.R. Rakshith},
title = {On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {127-140},
zbl = {1329.05184},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1850}
}
Chandrashekar Adiga; B.R. Rakshith. On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 127-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1850/
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