Zagreb Matrices in Terms of the Vertex-Degrees

The Zagreb matrices can also be considered the vertex- and edge-weighted matrices related to the vertex- and edge-connectivity matrices discussed above. They can be formulated in terms of the vertex- or edge-degrees. 

The vertex-Zagreb matrix, denoted by ZM, is a diagonal VxVmatrix defined in terms of the vertex-degrees d  

Summation of the diagonal elements gives the first Zagreb index. This index is discussed in a number of reports (Gutman and Trinajstid, 1972, Gutman et al., 1975, 

Sununation of the off-diagonal elements in the upper (or lower) matrix-triangle produces the second Zagreb index. This molecular descriptor is also discussed 

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Variable Zagreb Matrices in Terms of the Vertex-Degrees AND Edge-Degrees... 

Variable Zagreb matrices in terms of the vertex-degrees VZM and the edge-degrees WZM are given by (Milicevid and Nikolid, 2004 Milicevid et al., 2004 Nikolid etal.,2004) ... 

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