On the Determinant of the Adjacency Matrix of a Type of Plane Bipartite Graphs
نویسندگان
چکیده
Let G be a simple graph and A(G) its adjacency matrix. Based on some results of Rara (H. M. Rara, Discr. Math. 151 (1996) 213–219), we show that the determinant of A(G) of a plane graph G which has the property that every face-boundary is a cycle of size divisible by 4, equals −1, 0 or 1, provided the inner dual graph of G is a tree. As applications, we compute the algebraic structure count of some polygonal chains.
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