The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Let d 3 and n Let C(p) be the caterpillar obtained from the stars S p 1 +1 , S p 2 +1 , . . . , S p d-1 +1
On products and line graphs of signed graphs, their eigenvalues and energy
β Scribed by K.A. Germina; Shahul Hameed K; Thomas Zaslavsky
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 320 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A number of analogies which exist between the net signs and the eigenvaiues of molecular graphs are pointed out. In particular, a pairing-theorem-type regularity holds for the net signs of bipartite graphs (i.e. molecular graphs of altemant hydrocarbons).
## Abstract Our object is to enumerate graphs in which the points or lines or both are assigned positive or negative signs. We also treat several associated problems for which these configurations are selfβdual with respect to sign change. We find that the solutions to all of these counting problem
A graph is called of type k if it is connected, regular, and has k distinct eigenvalues. For example graphs of type 2 are the complete graphs, while those of type 3 are the strongly regular graphs. We prove that for any positive integer n, every graph can be embedded in n cospectral, non-isomorphic