Characterizes maximum and minimum vertex degree sums in planar (n, m)-graphs, indicating key properties.
A simple graph G with n vertices and m edges is called an (n, m)-graph.We study the sum of squares of the vertex degrees of planar (n, m)-graphs and characterize those attaining maximum value.Moreover, we determine the degree sequences of planar graphs with the minimum value of this sum.
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Horoldagva et al. (2026) studied this question.
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