Affiliation:
1. Department of Mathematics, Technion – Israel Institute of Technology , Haifa 32000 , Israel
Abstract
Abstract
We consider two types of joins of graphs
G
1
{G}_{1}
and
G
2
{G}_{2}
,
G
1
⊻
G
2
{G}_{1}\hspace{0.33em}⊻\hspace{0.33em}{G}_{2}
– the neighbors splitting join and
G
1
∨
=
G
2
{G}_{1}\mathop{\vee }\limits_{=}{G}_{2}
– the nonneighbors splitting join, and compute the adjacency characteristic polynomial, the Laplacian characteristic polynomial, and the signless Laplacian characteristic polynomial of these joins. When
G
1
{G}_{1}
and
G
2
{G}_{2}
are regular, we compute the adjacency spectrum, the Laplacian spectrum, the signless Laplacian spectrum of
G
1
∨
=
G
2
{G}_{1}\mathop{\vee }\limits_{=}{G}_{2}
, and the normalized Laplacian spectrum of
G
1
⊻
G
2
{G}_{1}\hspace{0.33em}⊻\hspace{0.33em}{G}_{2}
and
G
1
∨
=
G
2
{G}_{1}\mathop{\vee }\limits_{=}{G}_{2}
. We use these results to construct nonregular, nonisomorphic graphs that are cospectral with respect to the four matrices: adjacency, Laplacian, signless Laplacian and normalized Laplacian.
Cited by
3 articles.
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