An 
-firecracker
graph is a graph obtained by the concatenation of 
-stars by linking one tree
leaf from each to form a path graph (Chen et
al. 1997, Gallian 2026).
For positive integers 
and 
with 
, an 
-firecracker graph has 
vertices and 
edges. It is a tree,
and therefore a bipartite graph with chromatic
number 2.
Firecracker graphs are graceful (Chen et al. 1997, Gallian 2026).
Precomputed properties of firecrackers are implemented in the Wolfram Language as GraphData[{"Firecracker", {n, k}}].
