A twin edge k-coloring of a graph G is a proper edge k-coloring of G with the elements of Zk so that the induced vertex k-coloring, in which the color of a vertex v in G is the sum in Zk of the colors of the edges incident with v, is a proper vertex k-coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Twin chromatic index of the square P 2 n ...

Estimating the relative importance of vertices and edges is a fundamental issue in the analysis of complex networks, and has found vast applications in various aspects, such as social networks, power grids, and biological networks. Most previous work focuses on metrics of vertex importance and methods for identifying powerful vertices, while related work for edges is much lesser, especially for...

This paper presents an improved adaptive Wiener filtering algorithm for super-resolution reconstruction. When interpolating the high resolution pixels, the proposed algorithm locally adjusts the correlation model of the pixels by taking edge information into account. Simulation results show that the proposed algorithm produces SR outputs of better quality, both subjectively and objectively, as ...

In this paper we study the behavior of the second edge-Wiener index under the join and corona product of graphs. Results are applied for some classes of graphs such as suspensions, bottlenecks, and thorny graphs. 2010 Mathematics Subject Classification: 05C12; 05C62; 92E10

The general sum-connectivity index of a graph $G$ is defined as $chi_{alpha}(G)= sum_{uvin E(G)} (d_u + d_{v})^{alpha}$ where $d_{u}$ is degree of the vertex $uin V(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $chi_{alpha}$ values from a certain collection of polyomino ...

It is proved that the Wiener index of a weighted graph (G, w) can be expressed as the sum of the Wiener indices of weighted quotient graphs with respect to an arbitrary combination of Θ∗-classes. Here Θ∗ denotes the transitive closure of the Djoković-Winkler’s relation Θ. A related result for edge-weighted graphs is also given and a class of graphs studied in [19] is characterized as partial cu...

The atom-bond connectivity index is a recently introduced topological index defined as [Formula: see text], where du denotes degree of vertex u. Here we define a new version of the ABC index as [Formula: see text], where nu denotes the number of vertices of G whose distances to vertex u are smaller than those to other vertex v of the edge e = uv, and nv is defined analogously. The goal of this ...

Let G be a connected (molecular) graph with the vertex set V(G)={v1,⋯,vn}, and let di σi denote, respectively, degree transmission of vi, for 1≤i≤n. In this paper, we aim to provide new matrix description celebrated Wiener index. fact, introduce Wiener–Hosoya G, which is defined as n×n whose (i,j)-entry equal σi2di+σj2dj if vi vj are adjacent 0 otherwise. Some properties, including upper lower ...

‎In this paper we defined the vertex removable cycle in respect of the following‎, ‎if $F$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$G in F $‎, ‎the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $.‎ ‎The vertex removable cycles of eulerian graphs are studied‎. ‎We also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎    

Let G be a connected graph with vertex set V (G) and edge set E(G). The eccentric connectivity index of G, denoted by ξc(G), is defined as ∑ v∈V (G) deg(v)ec(v), where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. In this paper, we propose the edge version of the above index, the edge eccentric connectivity index of G, denoted by ξc e(G), which is defined as ξc e(G) = ∑ f∈E(...