نتایج جستجو برای: edge pair sum graph

تعداد نتایج: 470775  

Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...

For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...

Journal: :Graphs and Combinatorics 2016
Ruonan Li Bo Ning Shenggui Zhang

Let G be an edge-colored graph and v a vertex of G. The color degree of v is the number of colors appearing on the edges incident to v. A rainbow triangle in G is one in which all edges have distinct colors. In this paper, we first prove that an edge-colored graph on n vertices contains a rainbow triangle if the color degree sum of any two adjacent vertices is at least n+ 1. Afterwards, we char...

Journal: :iranian journal of mathematical chemistry 2016
m. azari

the vertex-edge wiener index of a simple connected graph g is defined as the sum of distances between vertices and edges of g. two possible distances d_1(u,e|g) and d_2(u,e|g) between a vertex u and an edge e of g were considered in the literature and according to them, the corresponding vertex-edge wiener indices w_{ve_1}(g) and w_{ve_2}(g) were introduced. in this paper, we present exact form...

Journal: :transactions on combinatorics 2015
n. paramaguru r. sampathkumar

let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

The sum of distances between all the pairs of vertices in a connected graph is known as the {it Wiener index} of the graph. In this paper, we obtain the Wiener index of edge complements of stars, complete subgraphs and cycles in $K_n$.

Journal: :Discrete Applied Mathematics 2007
Amitabha Tripathi Sujith Vijay

Let G be a finite simple graph with n vertices. The degree of a vertex v, which we write as deg v, is the number of vertices of G adjacent to v. Since there can be at most one edge between any pair of vertices in a simple graph, deg v ≤ n− 1 for each vertex v. One of the most basic results in Graph Theory, which is also easy to prove, is that if we sum the degrees of vertices of a finite simple...

2004
Takeshi Sugiyama T. SUGIYAMA

Let G be a graph of order n. A graph is linear forest if every component is a path. Let S be a set of m edges of G that induces a linear forest. An edge xy ∈ E(G) is called an S-edge if xy ∈ S. An S-edge-length of a cycle in G is defined as the number of S-edges that it contains. We prove that if the degree sum in G of every pair of nonadjacent vertices of G is at least n + m, then G contains h...

2004
Bang Ye Wu Kun–Mao Chao

Consider the following problem in network design: given an undirected graph with nonnegative delays on the edges, the goal is to find a spanning tree such that the average delay of communicating between any pair using the tree is minimized. The delay between a pair of vertices is the sum of the delays of the edges in the path between them in the tree. Minimizing the average delay is equivalent ...

The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...

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