Developing efficient algorithms for decentralized systems has been a popular research area in recent years. Among them, gossiping algorithms have been proven to be successful [Scaman et al., 2017, Duchi et al., 2011, Nedic and Ozdaglar, 2009]. In this approach, each client computes iteratively a weighted average of local estimators and network-wide estimators obtained from neighbors. The goal is to derive an estimator that converges to the average of the true values across the entire system. The weights are represented by a matrix that respects the graph structure under certain conditions. The gossiping-based averaging approach enables the incorporation of MAB methods in decentralized settings. In particular, motivated by the success of the UCB algorithm [Auer et al., 2002a] in stochastic MAB, [Landgren et al., 2016a,b, 2021, Zhu et al., 2020, 2021a,b, Martínez-Rubio et al., 2019, Chawla et al., 2020, Wang et al., 2021] import it to various decentralized settings under the assumption of sub-Gaussianity, including homogeneous or heterogeneous rewards, different graph assumptions, and various levels of global information. The regret bounds obtained are typically of order  $\log T$ . However, most existing works assume that the graph is time-invariant under further conditions, which is often not the case. For example, [Wang et al., 2021] provide an optimal regret guarantee for complete graphs which are essentially a centralized batched bandit problem [Perchet et al., 2016]. Connected graphs are also considered, but [Zhu et al., 2020] assume that the rewards are homogeneous and graphs are time-invariant related to doubly stochastic matrices. In addition, [Martínez-Rubio et al., 2019] propose the DDUCB algorithm for settings with time-invariant graphs and homogeneous rewards, dealing with deterministically delayed feedback and assuming knowing the number of vertices and the spectral gap of the given graph. Meanwhile, [Jiang and Cheng, 2023] propose an algorithm C-CBGE that is robust to Gaussian noises and deals with client-dependent MAB, but requires time-invariant regular graphs. [Zhu et al., 2021b] propose a gossiping-based UCB-variant algorithm for time-invariant graphs. In this approach, each client maintains a weighted averaged estimator by gossiping, uses doubly stochastic weight matrices depending on global information of the graph, and adopts a UCB-based decision rule by constructing upper confidence bounds. Recently, [Zhu and Liu, 2023], revisit the algorithm and add an additional term to the UCB rule for time-varying repeatedly strongly connected graphs, assuming no global information. However, the doubly stochasticity assumption excludes many graphs from consideration. Our algorithm builds on the approach proposed by [Zhu et al., 2021b] with new weight matrices that do not require the doubly stochasticity assumption. Our weight matrices leverage more local graph information, rather than just the size of the vertex set as in [Zhu and Liu, 2023, Zhu et al., 2021b]. We introduce the terminology of the stopping time for randomly delayed feedback, along with new upper confidence bounds that consider random graphs and sub-exponentiality. This leads to smaller high probability regret bounds, and the algorithm only requires knowledge of the number of vertices that can be obtained at initialization or estimated as in [Martínez-Rubio et al., 2019].