Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class has been studied extensively and generalized in many different directions. Induced on with restricted runlengths as vertices define Fibonacci-run graphs. These have same number cubes, but fewer edges graph theoretical properties...

We consider the problem of finding a subgraph given graph minimizing sum functions at vertices evaluated their degrees. While is NP-hard already for bipartite graphs when are convex on one side and concave other, we have that all convex, can be solved in polynomial time any graph. also provide solutions with fixed arbitrary functions, but number either nondecreasing or nonincreasing. note gener...

symmetric division deg index is one of the 148 discrete adriatic indices that showed good predictive properties on the testing sets provided by international academy of mathematical chemistry.symmetric division deg index is defined by$$sdd(g) = sume left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right),$$where $d_i$ is the degree of vertex $i$ in graph $g$.in this pap...