Ladder Graph
المؤلف:
Ball, W. W. R. and Coxeter, H. S. M
المصدر:
Mathematical Recreations and Essays, 13th ed. New York: Dover, 1987.
الجزء والصفحة:
...
22-3-2022
1979
Ladder Graph
The 
-ladder graph can be defined as 
, where 
is a path graph (Hosoya and Harary 1993; Noy and Ribó 2004, Fig. 1). It is therefore equivalent to the 
grid graph. The ladder graph is named for its resemblance to a ladder consisting of two rails and 
rungs between them (though starting immediately at the bottom and finishing at the top with no offset).
Hosoya and Harary (1993) also use the term "ladder graph" for the graph Cartesian product 
, where 
is the complete graph on two nodes and 
is the cycle graph on 
nodes. This class of graph is however more commonly known as a prism graph.
Ball and Coxeter (1987, pp. 277-278) use the term "ladder graph" to refer to the graph known in this work as the ladder rung graph.
The ladder graph 
is graceful (Maheo 1980).
The chromatic polynomial, independence polynomial, and reliability polynomial of the ladder graph 
are given by
where 
. Recurrence equations for the chromatic polynomial, independence polynomial, matching polynomial, rank polynomial, and reliability polynomial are given by
REFERENCES
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, 1987.
Hosoya, H. and Harary, F. "On the Matching Properties of Three Fence Graphs." J. Math. Chem. 12, 211-218, 1993.
Maheo, M. "Strongly Graceful Graphs." Disc. Math. 29, 39-46, 1980.
Noy, M. and Ribó, A. "Recursively Constructible Families of Graphs." Adv. Appl. Math. 32, 350-363, 2004.
الاكثر قراءة في نظرية البيان
اخر الاخبار
اخبار العتبة العباسية المقدسة
