The Sum-Vertex-Connectivity Matrix

The sum-vertex-connectivity matrix, denoted by S, was introduced independently by Zhou and Trinajstid (2009, 2010a) and Randid et al. (2010). Randid et al. (2010) named this matrix the distance-weighted adjacency matrix. It is defined as follows  

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The sum-edge-connectivity matrix, denoted by S, of a graph G is the sum-vertex-connectivity matrix of the corresponding line graph L(G) (Ludid et al., 2014) ... 

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