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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.03905 |
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| _version_ | 1866917630700421120 |
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| author | K, Najiya V A V, Chithra |
| author_facet | K, Najiya V A V, Chithra |
| contents | Let $G $ be a graph on $p$ vertices with adjacency matrix $A(G)$ and degree matrix $D(G)$. For each $α\in [0, 1]$, the $A_α$-matrix is defined as $A_α(G) = αD(G) + (1 - α)A(G)$. In this paper, we compute the $A_α$-characteristic polynomial, $A_α$-spectra and $A_α$-energy of some non-regular graphs obtained from unary operations on graphs like middle graph, central graph, m-splitting, and closed splitting graph. Also, we determine the $A_α$-energy of regular graphs like m-shadow, closed shadow, extended bipartite double graph, iterated line graph and m-duplicate graph. Furthermore, we identified some graphs that are $A_α$-equieneregetic and $A_α$-borderenergetic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $A_α$-energy of graphs formed by some unary operations K, Najiya V A V, Chithra Combinatorics Let $G $ be a graph on $p$ vertices with adjacency matrix $A(G)$ and degree matrix $D(G)$. For each $α\in [0, 1]$, the $A_α$-matrix is defined as $A_α(G) = αD(G) + (1 - α)A(G)$. In this paper, we compute the $A_α$-characteristic polynomial, $A_α$-spectra and $A_α$-energy of some non-regular graphs obtained from unary operations on graphs like middle graph, central graph, m-splitting, and closed splitting graph. Also, we determine the $A_α$-energy of regular graphs like m-shadow, closed shadow, extended bipartite double graph, iterated line graph and m-duplicate graph. Furthermore, we identified some graphs that are $A_α$-equieneregetic and $A_α$-borderenergetic. |
| title | $A_α$-energy of graphs formed by some unary operations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.03905 |