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Construction of Albertson Cospectral and Albertson Equienergetic Graphs Using Graph Operations
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The energy of a graph is an invariant calculated as the sum of the absolute eigenvalues of its adjacency matrix. This concept extends to various types of energies derived from different graph‐related matrices. This paper explores the spectral properties of Albertson energy and Albertson spectra. We examine the relationship between the adjacency matrix and the Albertson matrix. We calculate the Albertson energy and spectra for edge corona,
F
‐sum graphs, and several other graph operations, facilitating the construction of families of graphs that are
A
l
b
‐cospectral and
A
l
b
‐equienergetic. Furthermore, we identify graphs that exhibit properties such as being
A
l
b
‐orderenergetic,
A
l
b
‐hypoenergetic, and
A
l
b
‐integral. Lastly, we present the construction of nonisomorphic, self‐complementary graphs that are
A
l
b
‐cospectral.
Title: Construction of Albertson Cospectral and Albertson Equienergetic Graphs Using Graph Operations
Description:
The energy of a graph is an invariant calculated as the sum of the absolute eigenvalues of its adjacency matrix.
This concept extends to various types of energies derived from different graph‐related matrices.
This paper explores the spectral properties of Albertson energy and Albertson spectra.
We examine the relationship between the adjacency matrix and the Albertson matrix.
We calculate the Albertson energy and spectra for edge corona,
F
‐sum graphs, and several other graph operations, facilitating the construction of families of graphs that are
A
l
b
‐cospectral and
A
l
b
‐equienergetic.
Furthermore, we identify graphs that exhibit properties such as being
A
l
b
‐orderenergetic,
A
l
b
‐hypoenergetic, and
A
l
b
‐integral.
Lastly, we present the construction of nonisomorphic, self‐complementary graphs that are
A
l
b
‐cospectral.
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