What is the chromatic number of K3,K4 and K5?
Answers
What is the chromatic number of K3,K4 and K5?mplete bipartite graph with m = 5 and n = 3
Vertices
n + m
Edges
mn
Radius
{\displaystyle \left\{{\begin{array}{ll}1&m=1\vee n=1\\2&{\text{otherwise}}\end{array}}\right.} \left\{{\begin{array}{ll}1&m=1\vee n=1\\2&{\text{otherwise}}\end{array}}\right.
Diameter
{\displaystyle \left\{{\begin{array}{ll}1&m=n=1\\2&{\text{otherwise}}\end{array}}\right.} \left\{{\begin{array}{ll}1&m=n=1\\2&{\text{otherwise}}\end{array}}\right.
Girth
{\displaystyle \left\{{\begin{array}{ll}\infty &m=1\vee n=1\\4&{\text{otherwise}}\end{array}}\right.} \left\{{\begin{array}{ll}\infty &m=1\vee n=1\\4&{\text{otherwise}}\end{array}}\right.
Automorphisms
{\displaystyle \left\{{\begin{array}{ll}2m!n!&n=m\\m!n!&{\text{otherwise}}\end{array}}\right.} \left\{{\begin{array}{ll}2m!n!&n=m\\m!n!&{\text{otherwise}}\end{array}}\right.
Chromatic number
2
Chromatic index
max{m, n}
Spectrum
{\displaystyle \{0^{n+m-2},(\pm {\sqrt {nm}})^{1}\}} \{0^{n+m-2},(\pm {\sqrt {nm}})^{1}\}
Notation
{\displaystyle K_{m,n}} K_{m,n}