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Further study on k-restricted edge connectivity and exact k-restricted edge connectivity of a graph

Inspired by the studies on conditional connectivity by Harary [ 1 ], we worked on [Formula: see text]-restricted edge connectivity of a graph [Formula: see text] [ 4 ]. The [Formula: see text]-restricted edge connectivity of a graph [Formula: see text] is the cardinality of a minimum edge-cut whose deletion disconnects the graph [Formula: see text] into components where each component has order at least [Formula: see text]. In this work, we take into account some results on [Formula: see text]-restricted edge connectivity and the novel parameter exact [Formula: see text]-restricted edge connectivity. In the definition of [Formula: see text]-restricted edge connectivity, we impose some extra constraints to achieve this parameter. In this paper, we consider some fundamental aspects of exact [Formula: see text]-restricted edge connectivity and how they relate to the [Formula: see text]-restricted edge connectivity.

World Scientific Pub Co Pte Ltd

Athira Chandran Roy John G. Suresh Singh

Discrete Mathematics, Algorithms and Applications

2024

Title: Further study on k-restricted edge connectivity and exact k-restricted edge connectivity of a graph

Description:

Inspired by the studies on conditional connectivity by Harary [ 1 ], we worked on [Formula: see text]-restricted edge connectivity of a graph [Formula: see text] [ 4 ].

The [Formula: see text]-restricted edge connectivity of a graph [Formula: see text] is the cardinality of a minimum edge-cut whose deletion disconnects the graph [Formula: see text] into components where each component has order at least [Formula: see text].

In this work, we take into account some results on [Formula: see text]-restricted edge connectivity and the novel parameter exact [Formula: see text]-restricted edge connectivity.

In the definition of [Formula: see text]-restricted edge connectivity, we impose some extra constraints to achieve this parameter.

In this paper, we consider some fundamental aspects of exact [Formula: see text]-restricted edge connectivity and how they relate to the [Formula: see text]-restricted edge connectivity.

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