Geometric and topological properties of the complementary prism networks Articles uri icon

publication date

  • May 2023

start page

  • 9555

end page

  • 9575

issue

  • 8

volume

  • 46

International Standard Serial Number (ISSN)

  • 0170-4214

Electronic International Standard Serial Number (EISSN)

  • 1099-1476

abstract

  • The complementary prism of G$$ G $$, denoted by GG?$$ G\overline{G} $$, is the graph obtained from the disjoint union of G$$ G $$ and G?$$ \overline{G} $$ by adding edges between the corresponding vertices of G$$ G $$ and G?$$ \overline{G} $$. In this paper, we study the hyperbolicity constant of GG?$$ G\overline{G} $$. In particular, we obtain upper and lower bounds for the hyperbolicity constant, and we compute its precise value for many graphs. Moreover, we obtain bounds and closed formulas for the general topological indices A(GG?)= n-ary sumation uv is an element of E(GG?)a(du,dv)$$ A\left(G\overline{G}\right)={\sum}_{uv\in E\left(G\overline{G}\right)}a\left({d}_u,{d}_v\right) $$ and B(GG?)= n-ary sumation u is an element of V(GG?)b(du)$$ B\left(G\overline{G}\right)={\sum}_{u\in V\left(G\overline{G}\right)}b\left({d}_u\right) $$ (where du$$ {d}_u $$ denotes the degree of the vertex u,a$$ u,a $$ is a symmetric function with real values, and b$$ b $$ is a function with real values), and the generalized Wiener index W lambda(GG?)$$ {W}{\lambda}\left(G\overline{G}\right) $$, of complementary prisms networks. Finally, we performed a numerical study of the generalized Wiener index on random graphs

subjects

  • Mathematics

keywords

  • complementary prisms; generalized prism network; gromov hyperbolicity; geodesics