Edge Quasi $λ$-distance-balanced Graphs in Metric Space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909225835298816 |
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| author | Aliannejadi, Zohreh Alamoti, Somayeh Shafiee |
| author_facet | Aliannejadi, Zohreh Alamoti, Somayeh Shafiee |
| contents | In a graph $A$, the measure $|M_g^A(f)|=m_g^A(f)$ for each arbitrary edge $f=gh$ counts the edges in $A$ closer to $g$ than $h$. $A$ is termed an edge quasi-$λ$-distance-balanced graph in a metric space (abbreviated as $EQDBG$), where a rational number ($>1$) is assigned to each edge $f=gh$ such that $m_g^A(f)=λ^{\pm1}m_h^A(f)$. This paper introduces and discusses these graph concepts, providing essential examples and construction methods. The study examines how every $EQDBG$ is a bipartite graph and calculates the edge-Szeged index for such graphs. Additionally, it explores their properties in Cartesian and lexicographic products. Lastly, the concept is extended to nicely edge distance-balanced and strongly edge distance-balanced graphs revealing significant outcomes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11876 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Edge Quasi $λ$-distance-balanced Graphs in Metric Space Aliannejadi, Zohreh Alamoti, Somayeh Shafiee Combinatorics In a graph $A$, the measure $|M_g^A(f)|=m_g^A(f)$ for each arbitrary edge $f=gh$ counts the edges in $A$ closer to $g$ than $h$. $A$ is termed an edge quasi-$λ$-distance-balanced graph in a metric space (abbreviated as $EQDBG$), where a rational number ($>1$) is assigned to each edge $f=gh$ such that $m_g^A(f)=λ^{\pm1}m_h^A(f)$. This paper introduces and discusses these graph concepts, providing essential examples and construction methods. The study examines how every $EQDBG$ is a bipartite graph and calculates the edge-Szeged index for such graphs. Additionally, it explores their properties in Cartesian and lexicographic products. Lastly, the concept is extended to nicely edge distance-balanced and strongly edge distance-balanced graphs revealing significant outcomes. |
| title | Edge Quasi $λ$-distance-balanced Graphs in Metric Space |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.11876 |