Topological Indices and f-Polynomials on Some Graph Products

Blaya, Ricardo Abreu; Bermudo, Sergio; Rodríguez, José M.; Tourís, Eva

doi:10.3390/sym13020292

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2021

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“…The differential of a graph and other kinds of differentials of a set were introduced in [2] , where dimensions are given for the differential of a graph. Additionally, this parameter has been studied in [1,[3][4][5][6][7][8][9]. In addition, the differential of the Cartesian product of graphs was studied in [10].…”

Section: Introductionmentioning

confidence: 99%

General Properties on Differential Sets of a Graph

Basilio¹,

Bermudo²,

Hernández-Gómez³

et al. 2021

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Let G=(V,E) be a graph, and let β∈R. Motivated by a service coverage maximization problem with limited resources, we study the β-differential of G. The β-differential of G, denoted by ∂β(G), is defined as ∂β(G):=max{|B(S)|−β|S|suchthatS⊆V}. The case in which β=1 is known as the differential of G, and hence ∂β(G) can be considered as a generalization of the differential ∂(G) of G. In this paper, upper and lower bounds for ∂β(G) are given in terms of its order |G|, minimum degree δ(G), maximum degree Δ(G), among other invariants of G. Likewise, the β-differential for graphs with heavy vertices is studied, extending the set of applications that this concept can have.

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