In this paper, we present a generalization of Tsallis relative operator entropy defined for positive operators and investigate some related properties. Some inequalities involving the generalized are pointed out as well.

Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language study variety of areas. Remarkably, one the key information-theoretic quantities is given by relative entropy, which quantifies how difficult tell apart two probability distribut...

Let G be a group of order mu and U a normal subgroup of G of order u. Let G/U = {U1, U2, · · · , Um} be the set of cosets of U in G. We say a matrix H = [hij ] order k with entries from G is a quasi-generalized Hadamard matrix with respect to the cosets G/U if ∑ 1≤t≤k hith −1 jt = λij1U1 + · · · + λijmUm (∃λij1, · · · , ∃λijm ∈ Z) for any i ̸= j. On the other hand, in our previous article we def...

The generalized k-connectivity κk(G) of a graph G was introduced by Chartrand et al. in 1984. It is natural to introduce the concept of generalized k-edge-connectivity, λk(G). For general k, the generalized k-edgeconnectivity of a complete graph is obtained. For k ≥ 3, tight upper and lower bounds of κk(G) and λk(G) are given for a connected graph G of order n, namely, 1 ≤ κk(G) ≤ n− k2 and 1 ≤...