Affiliations: [a] CASPAM Bahauddin Zakariya University Multan, Pakistan
| [b] Department of Mathematics, Presidency University, Kolkata, India
| [c] Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Al Ahsa, Saudi Arabia
| [d] Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, United Arab Emirates
Correspondence:
[*]
Corresponding author. U. Ali, CASPAM Bahauddin Zakariya University Multan, Pakistan. E-mail: uali@bzu.edu.pk.
Abstract: There are several approaches to lower the complexity of huge networks. One of the key notions is that of twin nodes, exhibiting the same connection pattern to the rest of the network. We extend this idea by defining a twin preserving spanning subgraph (TPS-subgraph) of a simple graph as a tool to compute certain graph related invariants which are preserved by the subgraph. We discuss how these subgraphs preserve some distance based parameters of the simple graph. We introduce a sub-skeleton graph on a vector space and examine its basic properties. The sub-skeleton graph is a TPS-subgraph of the non-zero component graph defined over a vector space. We prove that some parameters like the metric-dimension are preserved by the sub-skeleton graph.
