Summary

In the following table, only shortest paths IRS are considered, and n denotes the number of nodes of the graph.

IRS classes	Graphs
1-SLIRS	paths, complete graphs, d-dimensional grids,
	d-dimensional tori with each dimension of length $\leqs 4$,
	complete bipartite graphs Kp,q with $p,q \geqs 2$,
	unit interval graphs, hypercube, generalized hypercube
1-SIRS	trees, rings, outerplanars, interval graphs,
	d-dim. tori with the $2^{\mbox{\small nd}}$ largest dim. of length $\leqs 4$,
	2D-grids with column-wrap-around, graphs with $n \leqs 6$,
	chordal ring of degree 4 with chord length $\leqs 3$,
	unit arc-circular graphs, Kp,q with $p,q \geqs 1$
2-SLIRS	d-dimensional tori, almost all graphs
3-SIRS	2-trees, Petersen graph
2k+1-SIRS	k-trees
$\floor{3p/2+\gamma}$-SIRS	p-plane graphs of genus $\gamma$
$\Omega(n^{1/2-\varepsilon})$-IRS	Shuffle-Exchange, Cube Connected Cycles, Butterfly
$\floor{2\sqrt{n}}$-SIRS	chordal rings of degree 4
$\Omega(\sqrt{n})$-IRS	cubic planar, triangulated planar, series-parallel graphs
$\Omega(\sqrt{kn})$-IRS	graphs of treewidth k, $2 \leqs k \leqs (n/3)^{1/3}$
$\Omega(f(n))$-IRS	Star graph, with $f(n) = n((\log\log{n})/\log{n})^5$
$\Omega(m\!-\!n)$-IRS	worst-case graph with m edges, $n \leqs m \leqs 3n/2$
$\Omega(n)$-IRS	worst-case cubic graph
$\alpha(n)$-SLIRS	all graphs, with $\alpha(n) < n/4 + (1/4)\sqrt{2n\ln{(3n^2)}}$