The energy of a graph G, denoted by E(G), is defined to be the sum of absolute values of all eigenvalues of the adjacency matrix of G. Let G(n, l, p) denote the set of all unicyclic graphs on n vertices with girth and pendent vertices being l ( 3) and p ( 1), respectively. More recently, one of the
Note on unicyclic graphs with given number of pendent vertices and minimal energy
β Scribed by Bofeng Huo; Shengjin Ji; Xueliang Li
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 166 KB
- Volume
- 433
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
This note presents a solution to the following problem posed by Chen, Schelp, and SoltΓ©s: find a simple graph with the least number of vertices for which only the degrees of the vertices that appear an odd number of times are given.
## Abstract For a vertex __v__ of a graph __G__, we denote by __d__(__v__) the __degree__ of __v__. The __local connectivity__ ΞΊ(__u, v__) of two vertices __u__ and __v__ in a graph __G__ is the maximum number of internally disjoint __u__ β__v__ paths in __G__, and the __connectivity__ of __G__ is
The Hosoya index and the Merrifield-Simmons index of a graph are defined as the total number of the matchings (including the empty edge set) and the total number of the independent vertex sets (including the empty vertex set) of the graph, respectively. Let W n,k be the set of connected graphs with
For every positive integer c , we construct a pair G, , H, of infinite, nonisomorphic graphs both having exactly c components such that G, and H, are hypomorphic, i.e., G, and H, have the same families of vertex-deleted subgraphs. This solves a problem of Bondy and Hemminger. Furthermore, the pair G