Table 1 Frequently used notations

G = (V, E, W)

Undirected and edge weighted graph

n = |V|, m = |E|

Number of vertices and number of edges

n \(_{X}\)= \(|V_{X}|\), m\(_{X}\) = |E\(_{X}|\)

Number of vertices and number of edges in subgraph X

nb(v)

The set of neighbors of v

d(v)

The degree of v

sup(e,H)

The support of edge e in subgraph H

\(\omega ({e})\)

The weight of edge e

f(H)

The weight of subgraph H \(\hbox {min}_{{e}\in \hbox {E}_{\mathrm{H}}}\{\omega ({e})\}\)

S\(_{(u,v)}\)

The common neighbors of vertex (u, v), \(nb(u) \cap nb(v)\)

\(\tau (H)\)

The trussness of subgraph H

E\({_{S}}_{(u,v)}\leftrightarrow {u,v}\)

The set of edges between \({_{S}}_{(u,v)}\) and {u, v}