Spectra of some new extended corona

Abstract

For two graphs G and H with n and m vertices, the corona G • H of G and H is the graph obtained by taking one copy of G and n copies of H and then joining the i th vertex of G to every vertex in the i th copy of H. The neighborhood corona G ⋆ H of G and H is the graph obtained by taking one copy of G and n copies of H and joining every neighbor of the i th vertex of G to every vertex in the i th copy of H. In this paper, we define four new extensions of corona and neighborhood corona of two graphs G and H; named the identity-extended corona, identity-extended neighborhood corona, neighborhood extended corona and neighborhood extended neighborhood corona and then determine the spectrum of their adjacency matrix, where H is a regular graph. As an application, we exhibit infinite families of integral graphs.

Spectra of (M,ℳ)-corona-join of graphs

“…corona) of G 1 and G 2 , and joining each vertex of the i-th copy of G 2 to every vertex of the j-th copy of G 2 , provided the vertices v i and v j are adjacent in G 1 . Following this, Tajarrod and Sistani [31] defined the following: Let V (G 2 ) = {v 1 , v 2 , . .…”

“…In [13,29] the authors defined the M -generalized corona of graphs constrained by vertex subsets and showed that it generalizes all the variants of corona of graphs defined in the literature except the variants of corona of graphs defined in [2,31]. Further, various spectra of the graphs constructed by this graph operation were obtained and the spectra of the variants of corona of graphs (except those mentioned above) were deduced.…”