On the spectral moment of graphs with given clique number

Abstract

Let ${\mathcal{L}}_{n,t}$ be the set of all $n$-vertex connected graphs with clique number $t$\,($2\le t\le n)$. For $n$-vertex connected graphs with given clique number, lexicographic ordering by spectral moments ($S$-order) is discussed in this paper. The first ${\sum }_{i=1}^{\lfloor \frac{n-t-1}{3}\rfloor }(n-t-3i)+1$ graphs with $3\le t\le n-4$, and the last few graphs, in the $S$-order, among ${\mathcal{L}}_{n,t}$ are characterized. In addition, all graphs in ${\mathcal{L}}_{n,n}\bigcup {\mathcal{L}}_{n,n-1}$ have an $S$-order; for the cases $t=n-2$ and $t=n-3$ the first three and the first seven graphs in the set ${\mathcal{L}}_{n,t}$ are characterized, respectively.

12 pages, 3 figures

References in corpus (2)

• On the spectral moment of trees with given degree sequences
• On the spectral moment of graphs with $k$ cut edges

Cited by in corpus (1)

• On the spectral moments of trees with a given bipartition