TY - JOUR
ID - 14623
TI - The higher-order Sombor index
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - You, Meiling
AU - Deng, Hanyuan
AD - College of Mathematics and Statistics, Hunan Normal University
Changsha, Hunan 410081, P. R. China
Y1 - 2024
PY - 2024
VL - 9
IS - 3
SP - 579
EP - 594
KW - the higher order Sombor index
KW - tree
KW - degree
KW - extremal value
DO - 10.22049/cco.2023.28658.1654
N2 - Based on the geometric background of Sombor index and motivating by the higher order connectivity index and the Sombor index, we introduce the pathcoordinate of a path in a graph and a degree-point in a higher dimensional coordinate system, and define the higher order Sombor index of a graph. We first consider mathematical properties of the higher order Sombor index, show that the higher order connectivity index of a starlike tree is completely determined by its branches and that starlike trees with a given maximum degree which have the same higher order Sombor indices are isomorphic. Then, we determine the extremal values of the second order Sombor index for all trees with n vertices and characterize the corresponding extremal trees. Finally, the chemical importance of the second order Sombor index is investigated and it is shown that the new index is useful in predicting physicochemical properties with high accuracy compared to some well-established.
UR - http://comb-opt.azaruniv.ac.ir/article_14623.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14623_f60f8a2ae984bcb21f7626feb8c776a2.pdf
ER -