The number of caterpillars

نویسندگان

  • Frank Harary
  • Allen J. Schwenk
چکیده

A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoInt\ is removed. The number of nonisomorphic caterpillars with n + 4 points is 2n + 2 [n/21 . This neat formula is proved in two ways: first, as a special caoe of an application of Pblya’s enumerration theorem which counts graphs with integer-weightell points; secondly, 3y an appropriate labeling of the lines of the caterpillar.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Constructing Graceful Graphs with Caterpillars

A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...

متن کامل

Snakes and Caterpillars in Graceful Graphs

Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...

متن کامل

On the harmonic index and harmonic polynomial of Caterpillars with diameter four

The harmonic index H(G) , of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G. We present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in Caterpill...

متن کامل

Degree-Splittability of Multigraphs and Caterpillars

A multigraph is degree-splittable if it decomposes into two submultigraphs whose degree lists are the same, plus one leftover edge when the total number of edges is odd. We prove that a connected multigraph is degree-splittable if it has an even number of vertices of each odd degree. For caterpillars, we characterize the splittable caterpillars with diameter at most 4, provide a general suffici...

متن کامل

Optimal Trajectory Generation for a Robotic Worm via Parameterization by B-Spline Curves

In this paper we intend to generate some set of optimal trajectories according to the number of control points has been applied for parameterizing those using B-spline curves. The trajectories are used to generate an optimal locomotion gait in a crawling worm-like robot. Due to gait design considerations it is desired to minimize the required torques in a cycle of gait. Similar to caterpillars,...

متن کامل

The Game Chromatic Number of 1-Caterpillars

The game chromatic number of a graph is defined using a two players game. In 1993, Faigle et al. proved that the game chromatic number of trees is at most four. In this paper we investigate the problem of characterizing those trees with game chromatic number three, and setttle this problem for 1-caterpillars.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Mathematics

دوره 6  شماره 

صفحات  -

تاریخ انتشار 1973