Let G = (V,E) be a simple connected graph. The eccentric-distance sum of G is defined as ξ(G) = ∑ {u,v}⊆V (G) [e(u) + e(v)]d(u, v), where e(u) is the eccentricity of the vertex u in G and d(u, v) is the distance between u and v. In this paper, we establish formulae to calculate the eccentric-distance sum for some graphs, namely wheel, star, broom, lollipop, double star, friendship, multi-star g...

Owing to the difficulty of direct observation, mergers of intermediate-mass black hole binaries are relatively less understood compared to stellar-mass binaries; however, the gravitational waves from their last few orbits and ringdown fall in the band of ground-based detectors. Because the typical source is expected to circularize prior to entering LIGO or VIRGO’s range, inspiral searches conce...

in this study, the effective parameters on the inelastic response of asymmetric buildings is evaluated for an ensemble of real iranian earthquake records by considering soil-structure interaction. then, the design eccentricity obtained from the inelastic dynamic soil-structure analysis is compared with the design eccentricity of seisimic codes of iran, atc-3, new zeland, canada, mexico, austral...

Abstract. In this paper the idea of sum distance which is a metric, in a fuzzy graph is introduced. The concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied using this metric. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterization of self centered complete fuzzy graph is obtained and conditions under which...

• Introduce several new distance-based global and local functions based the smallest distance which are related to eccentricity, center, sum of eccentricities in graphs trees. The values acompared with some sharp bounds established. difference between eccentricity uniformity behaves a very similar way as itself. Motivated from study trees, we introduce on vertex leaf (called “uniformity” at tha...

Let G be a simple graph with order n and size m. The quantity $$M_1(G)=\sum _{i=1}^{n}d^2_{v_i}$$ is called the first Zagreb index of G, where $$d_{v_i}$$ degree vertex $$v_i$$ , for all $$i=1,2,\dots ,n$$ . signless Laplacian matrix $$Q(G)=D(G)+A(G)$$ A(G) D(G) denote, respectively, adjacency diagonal degrees G. $$q_1\ge q_2\ge \dots \ge q_n\ge 0$$ eigenvalues largest eigenvalue $$q_1$$ spectr...

We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when p 6= 2. We get around this difficulty by working with certain...

In a recent paper Gunnells, Scott and Walden have determined the complete spectrum of the Schreier graph on the symmetric group corresponding to the Young subgroup Sn−2 × S2 and generated by initial reversals. In particular they find that the first nonzero eigenvalue, or spectral gap, of the Laplacian is always 1, and report that “empirical evidence” suggests that this also holds for the corres...

For a simple graph G, let e(G) denote the number of edges and Sk(G) denote the sum of the k largest eigenvalues of the signless Laplacian matrix of G. We conjecture that for any graph G with n vertices, Sk(G) ≤ e(G) + k+1 2 for k = 1, . . . , n. We prove the conjecture for k = 2 for any graph, and for all k for regular graphs. The conjecture is an analogous to a conjecture by A.E. Brouwer with ...