23,567 research outputs found
Distance-two labelings of digraphs
For positive integers , an -labeling of a digraph is a
function from into the set of nonnegative integers such that
if is adjacent to in and if
is of distant two to in . Elements of the image of are called
labels. The -labeling problem is to determine the
-number of a digraph , which
is the minimum of the maximum label used in an -labeling of . This
paper studies - numbers of digraphs. In particular, we
determine - numbers of digraphs whose longest dipath is of
length at most 2, and -numbers of ditrees having dipaths
of length 4. We also give bounds for -numbers of bipartite
digraphs whose longest dipath is of length 3. Finally, we present a linear-time
algorithm for determining -numbers of ditrees whose
longest dipath is of length 3.Comment: 12 pages; presented in SIAM Coference on Discrete Mathematics, June
13-16, 2004, Loews Vanderbilt Plaza Hotel, Nashville, TN, US
Distance two labeling of direct product of paths and cycles
Suppose that is a set of non-negative
integers and . The -labeling of graph is the function
such that if the distance
between and is one and if the
distance is two. Let and let
be the maximum value of Then is called number
of if is the least possible member of such that maintains an
labeling. In this paper, we establish numbers of graphs for all and .Comment: 13 pages, 9 figure
Classifying Families of Character Degree Graphs of Solvable Groups
We investigate prime character degree graphs of solvable groups. In
particular, we consider a family of graphs constructed by
adjoining edges between two complete graphs in a one-to-one fashion. In this
paper we determine completely which graphs occur as the prime
character degree graph of a solvable group.Comment: 7 pages, 5 figures, updated version is reorganize
- β¦