Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897912 | Linear Algebra and its Applications | 2018 | 9 Pages |
Abstract
The signature s(G) of a graph G is defined as the difference between its positive inertia index and the negative inertia index. In 2013, H. Ma et al. (2013) [8] conjectured that âc3(G)â¤s(G)â¤c5(G) for an arbitrary simple graph G, where ci(G) denotes the number of cycles in G with length i modulo 4. In 2014, L. Wang et al. [10] proved that âc3(Tk)â¤s(Tk)â¤c5(Tk) for any tree T and for any kâ¥2. In this paper, we prove that âc3(Gk)â¤s(Gk)â¤c5(Gk) for any simple graph G and for any kâ¥2, thus extend the main result of [10] to more general cases.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xiaobin Ma, Xianya Geng,