The Moore bound M(k, g) is a lower bound on the order of k-regular graphs of girth g (denoted (k, g)-graphs). The excess e of a (k, g)-graph of order n is the difference n −M(k, g). In this paper we consider the existence of (k, g)-bipartite graphs of excess 4 by studying spectral properties of their adjacency matrices. For a given graph G and for the integers i with 0 6 i 6 diam(G), the i-dist...

Let $A(G)$ and $D(G)$ be the adjacency matrix degree of $G$, respectively. For any real $\alpha \in [0,1]$, Nikiforov defined $A_{\alpha}(G)$ as \[ A_{\alpha}(G) = \alpha D(G) + (1-\alpha) A(G). \] In this paper, we generalize some previous results about $A_{1/2}$-spectral radius bicyclic graphs with a given sequence. Furthermore, characterize all extremal which have largest $A_{\alpha}$-spectr...

Bicyclic aziridines show exclusive photochromic behavior. Here, we summarize the results of optical and electrochemical properties, such as photochemical, solvatochromic, electrochromic andkinetic behavior of bicyclic aziridines linked to chalcone moieties. The photochromic process for conversion of closed photoisomers to open photoisomers for compounds 1-10 followed zero-order kinetics. For co...

Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees adjacent vertices graph Ω provides multiplicative first Zagreb index graph. In context theory, generalized is defined as product sum αth powers vertex Ω, where α real number such that α≠0 and α≠1. The focus this work extremal for several classes including trees, unicyclic,...