On two Laplacian matrices for skew gain graphs

Gain graphs are where the edges given some orientation and labeled with elements (called gains) from a group so that gains inverted when we reverse direction of edges. Generalizing notion gain graphs, skew have property reversed edge is image under an anti-involution. In this paper, study two different types, Laplacian g -Laplacian matrices for graph taken multiplicative F x field characteristic zero. Defining incidence matrix, also prove matrix tree theorem in case matrix.