February 9, 2023

# Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences

## Research

 Title The Laplacian characteristic polynomial of some bicyclic graphs and its applications Type Presentation Keywords Laplacian eigenvalue; multiplicity; characteristic polynomial; bicyclic Researchers a { color: #4f98b0; } a:hover { color: #ffab00; } a:link:visited { text-decoration: none; } Masoumeh Farkhondeh (First researcher) , Doost Ali Mojdeh (Second researcher) , Mohammad Habibi (Third researcher)

## Abstract

All graphs in this paper are nite and undirected with no loops or multiple edges. Let G be a graph. The Laplacian matrix of G is L(G) = D(G)􀀀A(G), where D(G) = diag(d(v1); : : : ; d(vn)) is a diagonal matrix and d(v) denotes the degree of the vertex v in G and A(G) is the ad- jacency matrix of G. A one-edge connection of two graphs G1 and G2 is a graph G with V (G) = V (G1) [ V (G2) and E(G) = E(G1) [ E(G2) [ fe = uvg where u 2 V (G1) and v 2 V (G2) is denoted by G = G1#G2. If M is a square matrix, then the minor of the entry in the i-th row and j-th column is the determinant of the submatrix formed by deleting the i-th row and j-th column. This number is often denoted Mi;j . We give a description of the some eigenvalues of L(G = G1#G2) and the relationship between the spectrums of L(G1), L(G2) and L(G = G1#G2), by the Laplacian characteristic polynomial of G.