A signed graph $(G,sigma)$ is a graph‎ ‎together with an assignment of signs ${+,-}$ to its edges where‎ ‎$sigma$ is the subset of its negative edges‎. ‎There are a few variants of coloring and clique problems of‎ ‎signed ...

We consider some combinatorics of elliptic root systems of type $A_1$. In particular, with respect to a fixed reflectable base, we give a precise description of the positive roots in terms of a ``positivity'' theorem. Also ...

‎‎The generalized Zagreb index is an extension of both ordinary and‎ ‎variable Zagreb indices‎. ‎In this paper‎, ‎we present exact formulae‎ ‎for the values of the generalized Zagreb index for product graphs‎. ‎Results are ...

Let $G=(V(G),E(G))$ be a digraph without loops and‎ ‎multiarcs‎, ‎where $V(G)={v_1,v_2,$ $ldots,v_n}$ and $E(G)$ are the‎ ‎vertex set and the arc set of $G$‎, ‎respectively‎. ‎Let $d_i^{+}$ be the‎ ‎outdegree of the vertex ...