The k-order Sombor Index Connected Graphs with Given Degree Sequence
For the simple connected graph G =(V,E),d(u)is the degree of the vertex u of G.The k-order Sombor index of G is defined as SOkα(G)=∑ uv∈E[d(u)k + d(v)k]α,k ∈{2,3,…,n}.The result shows that in the class of connected graphs with a fixed degree sequence(for which the minimum degree being equal to one),there exists a special extremal BFS-graph with minimum general Sombor index for 0<α<1 and maximum general Sombor index for either α>1or α<0.Moreover,for any given tree,unicyclic,and bicyclic degree sequences with minimum degree 1,there exists a unique extremal BFS-graph with minimum general Sombor index for 0<α<1 and maximum general Sombor index for either α>1or α<0.
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