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Here, we propose a dimension-independent multi-resolution model for Morse complexes built on a graph representation of the complexes, that we call a Multi-Resolution Morse Incidence Graph (MMIG).
A complete classification is given of pentavalent 3-geodesic-transitive graphs which are not 3-arc-transitive, which shows that a pentavalent 3-geodesic-transitive but not 3-arc-transitive graph is one of the following graphs: ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(2×6 -grid, H(5,2×6 -gridcosaH 5,2n, the icosahedronraph of the 2-(11,5,2)-desincidenceWells graph and the Sylvester graph.
Figure 3 shows the corresponding interaction (incidence) graph summarizing these interactions.
Onset dates were categorized according to work week for each year and were used to create an epidemic curve and yearly incidence graph.
It can be applied to (bio chemical systems where just the stoichiometric matrix is known (or even just the signs of its elements) or to signal transduction/gene regulatory networks represented by interaction graphs [ 18] (also called incidence graph [ 21] or causal influence graph [ 41]).
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We consider the metric dimension of two families of incidence graphs: incidence graphs of symmetric designs, and incidence graphs of symmetric transversal designs (i.e. symmetric nets).
These include strongly regular graphs, and incidence graphs of balanced incomplete block designs (BIBDs).
In this case, also incidence graphs of certain group divisible designs appear.
We also consider the relations between the incidence graphs of two-class partially balanced incomplete block designs and distance-regular graphs.
Next, we consider the relations between these graphs and two-class partially balanced incomplete block designs, and we present a number of situations when the graphs we consider are in fact the incidence graphs of those designs.
Next, we consider bipartite r-regular graphs with girth at least 6 whose second largest eigenvalue satisfies λ2⩽√r and prove that such graphs are the incidence graphs of two-class partially balanced incomplete block designs and also balanced incomplete block designs.
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