Common neighborhood energies and their relations with Zagreb index
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909118347870208 |
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| author | Jannat, Firdous Ee Nath, Rajat Kanti Das, Kinkar Chandra |
| author_facet | Jannat, Firdous Ee Nath, Rajat Kanti Das, Kinkar Chandra |
| contents | In this paper we establish connections between common neighborhood Laplacian and common neighborhood signless Laplacian energies and the first Zagreb index of a graph $\mathcal{G}$. We introduce the concepts of CNL-hyperenergetic and CNSL-hyperenergetic graphs and showed that $\mathcal{G}$ is neither CNL-hyperenergetic nor CNSL-hyperenergetic if $\mathcal{G}$ is a complete bipartite graph. We obtain certain relations between various energies of a graph. Finally, we conclude the paper with several bounds for common neighborhood Laplacian and signless Laplacian energies of a graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Common neighborhood energies and their relations with Zagreb index Jannat, Firdous Ee Nath, Rajat Kanti Das, Kinkar Chandra Combinatorics Spectral Theory 05C50 In this paper we establish connections between common neighborhood Laplacian and common neighborhood signless Laplacian energies and the first Zagreb index of a graph $\mathcal{G}$. We introduce the concepts of CNL-hyperenergetic and CNSL-hyperenergetic graphs and showed that $\mathcal{G}$ is neither CNL-hyperenergetic nor CNSL-hyperenergetic if $\mathcal{G}$ is a complete bipartite graph. We obtain certain relations between various energies of a graph. Finally, we conclude the paper with several bounds for common neighborhood Laplacian and signless Laplacian energies of a graph. |
| title | Common neighborhood energies and their relations with Zagreb index |
| topic | Combinatorics Spectral Theory 05C50 |
| url | https://arxiv.org/abs/2402.15416 |