Control and inverse problems in wave equations and graphs constitute a dynamic field at the intersection of applied mathematics, engineering and physics. This area investigates how waves ...

The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse ...

We investigate how the inverse degree index of graphs depends on their cyclomatic number. In particular, we provide sharp lower bounds on the inverse degree index over all graphs on a given number of ...

Learn how proportional relationships look on a graph, understand proportionality using worked examples, and for Higher tier, revise algebraic proportion.