On the characteristic polynomial of the Aa-matrix for some operations of graphs

被引：0

作者：

da Silva Junior, Joao Domingos Gomes ^{[1
,3
]}

Oliveira, Carla Silva ^{[1
,2
]}

da Costa, Liliana Manuela Gaspar Cerveira ^{[3
]}

机构：

[1] Ctr Fed Educ Tecnol Rio de Janeiro, Dept Engn Prod, Gen Canabarro 485, BR-20271204 Rio De Janeiro, RJ, Brazil

[2] Escola Nacl Ciencias Estat, Dept Matemat, Andre Cavalcanti 106, BR-20231050 Rio De Janeiro, RJ, Brazil

[3] Colegio Pedro II, Dept Matemat, Campo Sao Cristovao 177, BR-20921440 Rio De Janeiro, RJ, Brazil

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2023年 / 42卷 / 05期

关键词：

Aa-characteristic polynomial; Graph operations; Eigenvalue; A(ALPHA)-SPECTRAL RADIUS;

D O I：

10.1007/s40314-023-02329-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph of order n with adjacency matrix A(G) and diagonal matrix of degree D(G). For every a ? [0, 1], Nikiforov (Appl Anal Discrete Math 11(1):81-107, 2017) defined the matrix Aa(G) = aD(G) + (1 - a)A(G). In this paper, we present the A(a)(G)-characteristic polynomial when G is obtained by coalescing two graphs, and if G is a semi-regular bipartite graph we obtain the Aa-characteristic polynomial of the line graph associated with G. Moreover, if G is a regular graph, we exhibit the Aa-characteristic polynomial for the graphs obtained from some operations.

引用

页数：22

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