JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 56-63.doi: 10.6040/j.issn.1671-9352.0.2023.042

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Sombor index on four operation graphs

Yinzhen MEI(),Huifeng FU   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Received:2023-02-06 Online:2024-06-20 Published:2024-06-17

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Abstract:

Let G be a simple graph, E(G) be the edge set of G, and, du, dv be the degree of vertex u, v, respectively. In this paper, we focuse on the definition of F- sum of graphs combined with four transformation operations S(G), R(G), Q(G), T(G) and Cartesian product of two graphs, and calculate the upper bound of the Sombor index of the four kinds of related graphs by using the maximum degree and classification, and characterize their extreme values.

Key words: sombor index, graph operations, cartesian product, F-sum

CLC Number: 

  • O157.5

Fig.1

Example of S(P5), R(P5), Q(P5), T(P5)"

Fig.2

Example of G+FH"

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