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تسجيل مستخدم جديدThe scattering matrix with respect to an Hermitian matrix of a graph
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Recently, Gnutzmann and Smilansky presented a formula for the bond scattering matrix of a graph with respect to a Hermitian matrix. We present another proof for this Gnutzmann and Smilanskys formula by a technique used in the zeta function of a graph. Furthermore, we generalize Gnutzmann and Smilanskys formula to a regular covering of a graph. Finally, we define an $L$-fuction of a graph, and present a determinant expression. As a corollary, we express the generalization of Gnutzmann and Smilanskys formula to a regular covering of a graph by using its $L$-functions.
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