On the spectral radius and energy of the degree distance matrix of a connected graph
Let GG be a simple connected graph on nn vertices. The degree of a vertex v∈V(G)v\in V\left(G), denoted by dv{d}_{v}, is the number of edges incident with vv and the distance between any two vertices u,v∈V(G)u,v\in V\left(G), denoted by duv{d}_{uv}, is defined as the length of the shortest path from...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-04-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2025-0139 |
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| Summary: | Let GG be a simple connected graph on nn vertices. The degree of a vertex v∈V(G)v\in V\left(G), denoted by dv{d}_{v}, is the number of edges incident with vv and the distance between any two vertices u,v∈V(G)u,v\in V\left(G), denoted by duv{d}_{uv}, is defined as the length of the shortest path from uu to vv. The distance matrix of GG, denoted by, D(G)D\left(G), is defined as D(G)=duvD\left(G)={d}_{uv}. We now define and investigate the degree distance matrix of a connected graph GG, defined as MDD(G)=((du+dv)duv)u,v∈V(G){M}_{DD}\left(G)={\left(\left({d}_{u}+{d}_{v}){d}_{uv})}_{u,v\in V\left(G)}. In this article, first, we derive bounds for the largest eigenvalue of the degree distance matrix. Then, we establish some bounds for the energy of the degree distance matrix of GG. |
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| ISSN: | 2391-5455 |