A Study on Radio Labeling of Some Triangle-Free Graphs

Resumo

The co-channel interference are crucial when designing radio networks in a telecommunications sys
tem. We try to assign radio network transmitters channels so that the network satisfies all interference
constraints. Ale introduced the channel assignment problem, which involves assigning channels to the
transmitters. Refer to[1, 4] for further information on radio channel assignment. In radio networks,
the bandwidth allotted for the assignments determined by the frequency span, assuming that the fre
quencies are evenly distributed throughout the spectrum. In this instance, there is a strong correlation
between the geographic location of the transmitters and the interference between them. In the past,
radio network designers only took into account the two levels of interference—major and minor. If there
is significant interference between two transmitters, they are categorized as very close transmitters; if
there is little interference, they are classified as close transmitters. The interference graph is created and
channel assignment is transformed into graph labeling in order to solve the channel assignment problem.
The vertices in an interference graph represent the transmitters, and two vertices are connected by an
edge if the corresponding transmitters have major interference, two vertices have minor interference,
and corresponding vertices are at distance two if the transmitters are at distance three or farther away.
Put differently, vertices that are two distances apart represent close transmitters, while adjacent vertices
represent very close transmitters. Indeed, Roberts [2] suggested that two transmitters with minor inter
ference will receive different channels, and two transmitters with major interference will receive channels
that are at least two apart.