TY - JOUR ID - 1216 TI - Spectra of some new extended corona JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Tajarrod, Maliheh AU - Sistani, Tahereh AD - Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran Y1 - 2018 PY - 2018 VL - 5 IS - 2 SP - 23 EP - 34 KW - spectrum KW - corona KW - neighborhood corona KW - integral graphs DO - 10.22034/as.2018.1216 N2 - For two graphs $\mathrm{G}$ and $\mathrm{H}$ with $n$ and $m$ vertices, the corona $\mathrm{G}\circ\mathrm{H}$ of $\mathrm{G}$ and $\mathrm{H}$ is the graph obtained by taking one copy of $\mathrm{G}$ and $n$ copies of $\mathrm{H}$ and then joining the $i^{th}$ vertex of $\mathrm{G}$ to every vertex in the $i^{th}$ copy of $\mathrm{H}$. The neighborhood corona $\mathrm{G}\star\mathrm{H}$ of $\mathrm{G}$ and $\mathrm{H}$ is the graph obtained by taking one copy of $\mathrm{G}$ and $n$ copies of $\mathrm{H}$ and joining every neighbor of the $i^{th}$ vertex of $\mathrm{G}$ to every vertex in the $i^{th}$ copy of $\mathrm{H}$. In this paper, we define four new extensions of corona and neighborhood corona of two graphs $\mathrm{G}$ and $\mathrm{H}$; 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 $\mathrm{H}$ is a regular graph. As an application, we exhibit infinite families of integral graphs. UR - https://as.yazd.ac.ir/article_1216.html L1 - https://as.yazd.ac.ir/article_1216_0a6cc5868240f0394988d16861c2cbc9.pdf ER -