Graphical parameters for classes of tumbling block graphs

TL;DR

This paper introduces tumbling block graphs, a class of planar bipartite graphs with specific degree properties, and studies various graphical parameters for both infinite and finite instances.

Contribution

It defines tumbling block graphs and analyzes their graphical parameters, providing new insights into their structure and properties.

Findings

Tumbling block graphs are bipartite, planar, with degree 3 and 6 vertices.

The paper characterizes various graphical parameters for these graphs.

Finite and infinite tumbling block graphs exhibit distinct structural properties.

Abstract

The infinite tumbling block graph is a bipartite graph, where each vertex in one partite set is of degree 3 and each vertex in the other partite set is of degree 6. It is a 2-dimensional array of blocks of seven vertices and nine edges, a planar graph that has 3-D looks. This paper introduces tumbling block graphs and considers various graphical parameters for different classes of infinite and finite tumbling blocks.