Edge Quasi $\lambda$-distance-balanced Graphs in Metric Space
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-$\lambda$-distance-balanced graph in a metric space (abbreviated as $EQDBG$), where a rational number ($>1$) is assigned to each edge $f=gh$...
Saved in:
| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
07.06.2024
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Summary: | 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-$\lambda$-distance-balanced graph in a metric space (abbreviated as
$EQDBG$), where a rational number ($>1$) is assigned to each edge $f=gh$ such
that $m_g^A(f)=\lambda^{\pm1}m_h^A(f)$. 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. |
|---|---|
| DOI: | 10.48550/arxiv.2406.11876 |