The spread of generalized reciprocal distance matrix

2022/07/07 by Liu, Hechao, Huang, Yufei
#05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.05181

Abstract

The generalized reciprocal distance matrix RD_α(G) was defined as RD_α(G)=αRT(G)+(1-α)RD(G), 0≤ α≤ 1. Let λ₁(RD_α(G))≥ λ₂(RD_α(G))≥ ⋯ ≥ λ_n(RD_α(G)) be the eigenvalues of RD_α matrix of graphs G. Then the RD_α-spread of graph G can be defined as S_RDα(G)=λ₁(RD_α(G))-λ_n(RD_α(G)). In this paper, we first obtain some sharp lower and upper bounds for the RD_α-spread of graphs. Then we determine the lower bounds for the RD_α-spread of bipartite graphs and graphs with given clique number. At last, we give the RD_α-spread of double star graphs. Our results generalize the related results of the reciprocal distance matrix and reciprocal distance signless Laplacian matrix.

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