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

Chandrashekar Adiga; B.R. Rakshith

Discussiones Mathematicae Graph Theory (2016)

  • Volume: 36, Issue: 1, page 127-140
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Chandrashekar Adiga, and B.R. Rakshith. "On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs." Discussiones Mathematicae Graph Theory 36.1 (2016): 127-140. <http://eudml.org/doc/276980>.

@article{ChandrashekarAdiga2016,
abstract = {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.},
author = {Chandrashekar Adiga, B.R. Rakshith},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {spectrum; corona; neighbourhood corona; edge corona; energy of a graph; equienergetic graphs},
language = {eng},
number = {1},
pages = {127-140},
title = {On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs},
url = {http://eudml.org/doc/276980},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Chandrashekar Adiga
AU - B.R. Rakshith
TI - On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 1
SP - 127
EP - 140
AB - 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.
LA - eng
KW - spectrum; corona; neighbourhood corona; edge corona; energy of a graph; equienergetic graphs
UR - http://eudml.org/doc/276980
ER -

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