# A note on minimum linear arrangement for BC graphs

## TL;DR

This paper addresses the minimum linear arrangement problem specifically for BC graphs, a family that includes various well-known cube-like graphs, providing solutions for optimal vertex labelings.

## Contribution

It offers the first solution to the minimum linear arrangement problem for BC graphs, encompassing multiple important graph families.

## Key findings

- Solved the minimum linear arrangement problem for BC graphs.
- Included various cube-based graph families such as hypercubes and twisted cubes.
- Provides optimal arrangements for these complex graph structures.

## Abstract

A linear arrangement is a labeling or a numbering or a linear ordering of the vertices of a graph. In this paper we solve the minimum linear arrangement problem for bijective connection graphs (for short BC graphs) which include hypercubes, M\"{o}bius cubes, crossed cubes, twisted cubes, locally twisted cube, spined cube, $Z$-cubes, etc. as the subfamilies.