abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

The set of all eigenvalues of a characteristic matrix of a graph, also referred to as the spectrum, is a well-known topology retrieval method. In this paper, we study the spectrum of the Laplacian matrix of an observable part of the Internet graph at the IPlevel, extracted from traceroute measurements performed via RIPE NCC and PlanetLab. In order to investigate the factors influencing the Lapl...

In this study, two new salicylideneaniline derivative compounds which are an isomer of each other have been synthesized and characterized by X-Ray Diffraction (XRD) technique, IR spectroscopy, and theoretical method. While (E)-4-(dihydroxyamino)-2-(((4-fluorophenyl)imino) methyl)phenol (1), crystalizes triclinic P-1 space group, (E)-4-(dihydroxyamino)-2-(((3-fluorophenyl)im...

the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.

The character of the electronic transitions in the ultraviolet-visible-near infrared (UV-vis-NIR) spectra of platinum-bis(alkynyl) bridged, bis-triarylamine mixed-valence systems trans-[Pt(C≡CC6H4NAr2)2 (PR3)2](n+) (R = ethyl, Ar = C6H4CH3-4 (1) or C6H4OCH3-4 (2); R = Ph, Ar = C6H4CH3-4 (3) or C6H4OCH3-4 (4), n = 0, 1, 2) has been determined from a combination of spectroscopic measurement and d...

Let Wn = K1 ∨ Cn−1 be the wheel graph on n vertices, and let S(n, c, k) be the graph on n vertices obtained by attaching n− 2c− 2k − 1 pendant edges together with k hanging paths of length two at vertex v0, where v0 is the unique common vertex of c triangles. In this paper we show that S(n, c, k) (c > 1, k > 1) and Wn are determined by their signless Laplacian spectra, respectively. Moreover, w...

the rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. let $r$ be a ring. let $mathbb{a}(r)$ denote the set of all annihilating ideals of $r$ and let $mathbb{a}(r)^{*} = mathbb{a}(r)backslash {(0)}$. the annihilating-ideal graph of $r$, denoted by $mathbb{ag}(r)$  is an undirected simple graph whose vertex set is $mathbb{a}(r)...

Let Ln be the hexagonal chain graph,Fn be the hexacyclic system graph and Mn be the Möbius hexacyclic system graph. Derflinger and Sofer gave the spectra of Ln and Fn by using group theoretical method. Later, Gutman gave the spectra of them using a polynomial result due to Godsil and McKay. In this paper, we give a simple and direct method to determine the characteristic polynomial and spectra ...