1. Concepts I have learned
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First, I have learned the basic knowledge in graphs such as its description,
components, and symbols. I have known that a graph is not only simply a graph of
function, but it is specifically described as a collection of vertices and edges
wherein points and lines can be observed. There are also symbols that we need to
be aware of. For instance, graph G is denoted by G where the set V(G) is called the
vertex set of G and the set E(G) is called the edge set of G. Hence- G=(V(G),E(G)).
Denotation p (order) refers to the number of vertices in a graph G while q (size)
pertains to the number of edges on a graph G.
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Second, through this module, I have known the different kinds of graph and what
they differ from each other. Trivial graph has on vertex and no edges; Simple graph
is with no loops and no two of its links join the same pair of vertices; Complete graph
can be seen when each pair of distinct vertices is joined by an edge – also a simple
graph. In contrast, when the graph has no edges, it is called an empty graph.
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Third, I have also learned about the Euler and Hamiltonian graphs. In simplest words,
a cycle that travels exactly once over each EDGE in a graph is called EULIRIAN.
While a cycle that travels exactly once over each VERTEX in a graph is called
HAMILTONIAN.
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Lastly, I have known different terms included in knowing graphs such as vertex,
edge, loop, incident, adjacent, walk, path, length, trail, and more.
2. Concepts that need some more exercise
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In order to provide us a more challenging yet comprehensive understanding of how
graphs work, I believe it is preferable if another set of activities are given for each
concept. We only relied on the PowerPoint, module and exercises and that we only
had a general knowledge of this topic. I would want to see more exercises covering
every concept to ensure that we really understand the lesson.
3. Insights
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For my insights in the mathematics of graph, I have learned that graphs specifically
the graph theory is ultimately the study of relationships. Given a set of nodes &
connections, which can abstract anything from city layouts to computer data,
graph theory provides a helpful tool to quantify & simplify the many moving parts of
dynamic systems. Studying graphs through a framework provides answers to many
arrangements, networking, optimization, matching and operational problems.
Graphs can be used to model many types of relations and processes in physical,
biological, social and information systems, and has a wide range of useful
applications.