barbaric, brutal, grisly, gruesome, horrific, savage, terrible, vicious, violent
cold-blooded, deliberate, premeditated, wilful/willful (law, esp. BrE)
a verdict of wilful murder

senseless
shocking, tragic
perfect
He committed the perfect murder and left no forensic evidence.

indiscriminate, random
systematic
wholesale
the wholesale murder of innocent citizens

first-degree, second-degree
aggravated
attempted
alleged, suspected
double, mass, multiple, serial, triple
ritual
terrorist
gangland (BrE)
racial, racist, sectarian
politically motivated, racially motivated, sexually motivated
judicial, state-sanctioned, state-sponsored
high-profile, notorious
mysterious
unsolved
capital, felony, statutory (all AmE,law)

carry out, commit, perpetrate (formal)
murders committed by terrorists

investigate, probe (esp. BrE)
solve
link
Detectives are linking the two murders.

imprison sb for, jail sb for
avenge
He vowed to avenge his brother's murder.

witness
implicate sb in
new evidence that implicated her in the murder

mastermind, orchestrate, plan, plot
advocate
order
He ordered the murder of his political opponents.

admit, deny
get away with (figurative)
They let their children get away with murder!

incite
condemn
condone, justify
Nothing justifies murder.

happen, occur, take place
shock sb
It was a murder which shocked the nation.

victim
suspect
detective, squad
case, hunt (informal), inquiry (esp. BrE), investigation, probe
charge
trial
conviction
attempt
plot
scene, site
weapon
campaign (esp. BrE), spree
count, rate, toll
a city that has the highest murder rate in the US

capital
The city used to be the murder capital of the world.

mystery, story
Her latest novel is a gripping murder mystery.

brutally, cruelly, in cold blood, savagely, violently
The boy was brutally murdered.
They were murdered in cold blood.

systematically
deliberately
allegedly

attempt to, try to
plan to, plot to

admit murdering sb, deny murdering sb
be accused of murdering sb, be charged with murdering sb
She was arrested and charged with murdering the two children.

be convicted of murdering sb, be found guilty of murdering sb
be found murdered
He was found murdered in the cemetery.

Murder is used with these nouns as the subject:
fanatic, killer, mob

Murder is used with these nouns as the object:
lover