On Comparing Variable Zagreb Indices for Unicyclic Graphs

Recently, the first and second Zagreb indices are generalized into the variable Zagreb indices which are defined by M-lambda(1)(G) = Sigma(u is an element of V)(d(u))(2 lambda) and M-lambda(2)(G) = Sigma(uv is an element of-E) (d(u)d(v))(lambda), where lambda is any real number. In this paper, we prove that M-lambda(1)(G)/n >= M-lambda(2)(G)/m for all unicyclic graphs and all lambda is an element of (-infinity, 0]. And we also show that the relationship of numerical value between M-lambda(1)(G)/n and M-lambda(2)(G)/m is indefinite in the distinct unicyclic graphs for each lambda is an element of(1 +infinity). With the conclusion in [4], we finish discussing the relationship of M-lambda(1)(G)/n and M-lambda(2)(G)/m in unicyclic graphs for lambda is an element of R.