linear algebra trail

order

number of vertices

size

number of edges

incident

edge has a vertex (is incident with vertex)

degree of v deg(v)

number of edges incident with v

maximum degree (delta G)

the highest degree among all vertices (greatest connected edges)

mimum degree (swirly thing G)

mimum number of connected edges

degree sequence of order n

descending order of vertex degrees, repeating how how many times each degree repeats

walk

sequence of vertices (not necessarily distinct)

path

vertices of walk are distinct

trail

edges in walk are distinct

cycle

closed path (distinct vertices) that begins and ends at same vertice

circuit

closed trail, walk of distinct edges that ends and begins at same place

length

number of edges, counting each repetition

connected

every pair of vertices can be joined by a path

complete

every vertex is adjacent to every other vertex (can touch with one edge), denoted by Kn (n is order)

regular

if every vertex has the same degree

subgraph

a graph that comes from part of another graph

bipartite

vertex set can be separated into two sets, X and Y, so that every edge has one end in X and one end in Y

complete bipartite graph

every edge has one end in each side (each of the vertex sets), and all possible connections between the sides are made, denoted by K(m, n) where m is order of set of X vertices and n is order of set of Y vertices

isomorphic

can be transformed into another graph where all edges and ajacencies are preserved

Eulerian

contains every edge only once

Hamiltonian

contains every vertex only once

planar

every interesection has a vertex