is a branch of mathematics created to solve problems involving the most efficient way to travel between different directions.

it was developed after _____ solved an eighteenth century problem in solving the seven bridges of _____ in a city now called _____ in a modern Russia.

is a set of points called ____ and line segments or curves called ____ that connect vertices.

is an edge that begins and ends at the same vertex.

is a line connecting two vertices called endpoints.

is the number of its vertices.

is the number of edges that intersect the vertex.

has an even number of edges that intersect the vertex.

has an odd number of edges that intersect the vertex.

pair of vertices joined by an edge.

term describing an edge if its joined to a vertex.

edge that begins and ends at the same vertex.

has two distinct endvertices.

graph with multiple edges; allowing more than one edge to connect between two vertices; such edges are called multiple edges.

graph with loops and multiple edges.

alternating sequences of vertices and edges, with each edge being incident to the vertices immediately preceding and succeeding it in the sequence.

walk with no repeated edges.

walk with no repeated vertices.

walk with its initial vertex as also its terminal vertex.

walk with its initial vertex different from its terminal vertex.

closed trail with at least one edge and no repeated vertices except that the initial vertex is the terminal vertex.

length of a shortest (simple) cycle in the graph.

length of the longest cycle in the graph.

number of edges in the sequence defining the walk; thus the length of a path or cycle is also the number of edges in the path or cycle.

graph in which every pair of its vertices is connected by a path; otherwise, the graph is disconnected.

A graph that is disconnected two or more pieces.

vertex whose removal disconnects the remaining subgraph.

edge whose removal disconnects the graph.

it can be drawn without any break in the curve and without repeating any edges.

A trail or circuit (or cycle) is ____ if it uses all edges precisely once.

A graph that contains an Eulerian trail is ____.

A graph is ____ if and only if the degree of each vertex is even.

is a graph whose edges have directions.

In a digraph, a pair of edges in which one is directed from vertex a to vertex b and the other is directed from vertex b to vertex a.

is a vertex with 0 in-degree.

is a vertex with 0 out-degree.

it associates a value (weight) with every edge in the graph

is a simple graph that if u and v are vertices in T, there exists a unique simple walk from u to v.

is connected and an acyclic graph.

a graph with no cycle.

a tree in which a particular vertex is designed as a root.

length of simple path from the root to a vertex v

maximum level number

the study of changes in the number of births, marriages, deaths, etc. in a particular area during a period of time

a British scholar who warned that the population growth will inevitably exhaust world food supply by the middle of the 19th century.

American biologist with his wife wrote ___ which argued that overpopulation in the 1970s and 80s will bring global environment disasters that would in turn lead to food shortage and mass starvation.

Critics of the neo-Malthusian theory who disagrees with Thomas Maltus’s prediction and accused governments of using population control as a substitute for social justice and much-needed reforms such as land distribution, employment creation, provision of mass education and health care, and emancipation.

should receive family planning counseling on abortion, the dangers of sexually transmitted diseases, the nature of human sexuality, and the main elements of responsible parenthood.

What are the cause of poverty?