Tetracyclic harmonic graphs

Abstract

A graph G on n vertices v1, v2,..., vn is said to be harmonic if (d(v1),d(v2),..., d(vn))t is an eigenvector of its (0,1)-adjacency matrix where d(vi) is the degree ?(= number of first neighbors) of the vertex Vi i = 1,2,..., n. Earlier all acyclic, unicyclic, bicyclic and tricyclic harmonic graphs were characterized. We now show that there are 2 regular and 18 non-regular connected tetracyclic harmonic graphs and determine their structures.