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تسجيل مستخدم جديدThe Q-index and connectivity of graphs
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A connected graph $G$ is said to be $k$-connected if it has more than $k$ vertices and remains connected whenever fewer than $k$ vertices are deleted. In this paper, for a connected graph $G$ with sufficiently large order, we present a tight sufficient condition for $G$ with fixed minimum degree to be $k$-connected based on the $Q$-index. Our result can be viewed as a spectral counterpart of the corresponding Dirac type condition.
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Let $G$ be a nonempty simple graph with a vertex set $V(G)$ and an edge set $E(G)$. For every injective vertex labeling $f:V(G)tomathbb{Z}$, there are two induced edge labelings, namely $f^+:E(G)tomathbb{Z}$ defined by $f^+(uv)=f(u)+f(v)$, and $f^-:E
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Let $G$ be a finite simple non-complete connected graph on ${1, ldots, n}$ and $kappa(G) geq 1$ its vertex connectivity. Let $f(G)$ denote the number of free vertices of $G$ and $mathrm{diam}(G)$ the diameter of $G$. Being motivated by the computatio
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