## Abstract

Given two connected graphs, G and H. The Order and size of Gand H, are u and v, and m and n, respectively. Graph G square edge-corona H, denoted by G ⋄^{2} H and defined as G ⋄^{2} H: = (G ⋄ H) ⋄ H, that is a graph obtained from G, the first v-copies of H that is H_{h}, with h ∈ {1,2,.., v], and the second v(1 + 2n + m)-copies of H that is H_{hk}, with h ∈ {1,2,.., v] and k ∈ {1,2,..,1 + 2n + m] and joining the terminal vertices of e_{h} ∈ E(G), with e_{h} = i_{h}j_{h} and i_{h}, j_{h} ∈ V(G), to all vertices of H_{h}, and then joining the terminal vertices of e_{k} = r_{k}s_{k}, e_{k} ∈ G ⋄ H, to all vertices of H_{hk} . In this paper, the spectrum of the adjacency, Laplacian, and signless-Laplacian matrices of the graph G ⋄^{2} H will be analyzed further.

Original language | English |
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Article number | 012012 |

Journal | Journal of Physics: Conference Series |

Volume | 1538 |

Issue number | 1 |

DOIs | |

Publication status | Published - 19 Jun 2020 |

Event | 3rd International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2019 - East Java, Indonesia Duration: 26 Oct 2019 → 27 Oct 2019 |