Geodesic
The relations between the Sombor index and Merrifield-Simmons index
Filomat, Tome 37 (2023) no. 14, p. 4785

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DOI

The Sombor index SO(G) of a graph G is defined as SO(G) = ∑ uv∈E(G) (dG(u)2 + dG(v)2) 1 2 , while the Merrifield-Simmons index i(G) of a graph G is defined as i(G) = ∑ k≥0 i(G; k), where dG(x) is the degree of any one given vertex x in G and i(G; k) denotes the number of k-membered independent sets of G. In this paper, we investigate the relations between the Sombor index and Merrifield-Simmons index. First, we compare the Sombor index with Merrifield-Simmons index for some special graph families, including chemical graphs, bipartite graphs, graphs with restricted number of edges or cut vertices and power graphs, and so on. Second, we determine sharp bounds on the difference between Sombor index and Merrifield-Simmons index for general graphs, connected graphs and some special connected graphs, including self-centered graphs and graphs with given independence number.
DOI : 10.2298/FIL2314785C
Classification : 05C07, 05C69
Keywords: Sombor index, Merrifield-Simmons index, Comparison, Difference, Bounds, Extremal graphs 
Yaojun Chen; Hongbo Hua. The relations between the Sombor index and Merrifield-Simmons index. Filomat, Tome 37 (2023) no. 14, p. 4785 . doi: 10.2298/FIL2314785C
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     title = {The relations between the {Sombor} index and {Merrifield-Simmons} index},
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     doi = {10.2298/FIL2314785C},
     language = {en},
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