<abstract xmlns="http://www.w3.org/1999/xhtml">

A graph G is said to be a semi-splitting block graph if there exists a graph H such that SB(H) ≌ G. This paper establishes a characterisation of semi-splitting block graphs based on the partition of the vertex set of G. The vertex (edge) connectivity and p-connectedness (p-edge connectedness) of SB(G) are examined. For all integers a, b with 1 &lt; a &lt; b, the existence of the graph G for which κ (G) = a, κ (SB(G)) = b and λ (G) = a, λ (SB(G)) = b are proved independently. The characterization of graphs with κ(SB(G)) = κ (G) and a necessary condition for graphs with κ (SB(G)) = λ (SB(G)) are achieved.
</abstract>

A graph G is said to be a semi-splitting block graph if there exists a graph H such that SB(H) ≌ G. This paper establishes a characterisation of semi-splitting block graphs based on the partition of the vertex set of G. The vertex (edge) connectivity and p-connectedness (p-edge connectedness) of SB(G) are examined. For all integers a, b with 1 < a < b, the existence of the graph G for which κ (G) = a, κ (SB(G)) = b and λ (G) = a, λ (SB(G)) = b are proved independently. The characterization of graphs with κ(SB(G)) = κ (G) and a necessary condition for graphs with κ (SB(G)) = λ (SB(G)) are achieved.

On connectivity of the semi-splitting block graph of a graph

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On connectivity of the semi-splitting block graph of a graph"}

A graph G is said to be a semi-splitting block graph if there exists a graph H such that SB(H) ≌ G. This paper establishes a characterisation of semi-splitting...

On connectivity of the semi-splitting block graph of a graph

Published Online: Aug 08, 2023

Page range: 170 - 180

Received: May 30, 2023

DOI: https://doi.org/10.2478/ausi-2023-0012

Keywords
semi-splitting block graph of a graph, vertex connectivity, edge connectivity

© 2023 Nivedha Baskar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On connectivity of the semi-splitting block graph of a graph

Published Online: Aug 08, 2023

Page range: 170 - 180

Received: May 30, 2023

DOI: https://doi.org/10.2478/ausi-2023-0012

Keywordssemi-splitting block graph of a graph, vertex connectivity, edge connectivity

© 2023 Nivedha Baskar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
semi-splitting block graph of a graph, vertex connectivity, edge connectivity