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, dn where d1 d2 dn. Determine (G K1).
please prove this for me
Let G be a graph with degree sequence d1, d2, . . . , dn where d1 ≥ d2 ≥· · · ≥ dn. Determine λ(G ∨ K1).
General information about G and K1 maybe will help:
A graph G has connectivity 0 if and only if either G = K1 or G is disconnected; a graph G has connectivity 1 if and only if G = K2 or G is a connected graph with cut-vertices; and a graph G has connectivity 2 or more if and only if G is a nonseparable graph of order 3 or more.
An edge-cut of minimum cardinality in G is a minimum edge- cut and this cardinality is the edge-connectivity of G, which is denoted by λ(G). The trivial graph K1 does not contain an edge-cut but we define λ(K1) = 0. Therefore, λ(G) is the minimum number of edges whose removal from G results in a disconnected or trivial graph.
