A characterization of graphs with interval two-step graphs
نویسندگان
چکیده
منابع مشابه
A Characterization of Graphs with Interval Two-Step Graphs
Dedicated by the other authors to Professor John Maybee on the occasion of his 65th birthday. Abstract. One of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. This problem originated in the work of Cohen 5, 6] on food webs. In this paper we consider this problem for the class of loopless symmetric digraphs. The competition graph ...
متن کاملA Characterization of Graphs with Interval Squares
The competition graph of a symmetric digraph D with a loop at each vertex is the square of the underlying graph of D with loops removed. In the interest of eeciently assigning radio frequencies in a communication network, we would like to determine which graphs have interval squares. Necessary and suucient conditions on the graph G are given for G 2 to be interval for several large classes of g...
متن کاملA CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a textit{metric basis} for $G$. The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$. Givi...
متن کاملA matrix characterization of interval and proper interval graphs
In this work a matrix representation that characterizes the interval and proper interval graphs is presented, which is useful for the efficient formulation and solution of optimization problems, such as the k-cluster problem. For the construction of this matrix representation every such graph is associated with a node versus node zero–one matrix. In contrast to representations used in most of t...
متن کاملGraphs with Metric Dimension Two-A Characterization
In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. 2 ) ( = G β ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever 2 ) (...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)00173-b