نتایج جستجو برای: vertex distance

تعداد نتایج: 274523  

Journal: :European Journal of Combinatorics 2009

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

Journal: :Mathematica Pannonica 2022

We treat a variation of graph domination which involves partition ( V 1 , 2 ,..., k ) the vertex set G and each class i over distance d where all vertices edges may be used in process. Strict upper bounds extremal graphs are presented; results collected three handy tables. Further, we compare high number classes dominators needed.

Journal: :Mathematics 2021

Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to local inclusive (respectively, non-inclusive) d-distance irregular of graph G if for any two adjacent vertices x,y∈V(G) their weights are distinct, where the weight x∈V(G) sum all labels whose distance from x at most d but least 1). The minimum k which there exists called irregularity strength G. In this paper, we p...

Journal: :Discrete Applied Mathematics 2015

A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...

Let G be a simple connected graph. The transmission of any vertex v of a graph G is defined as the sum of distances of a vertex v from all other vertices in a graph G. Then the distance signless Laplacian matrix of G is defined as D^{Q}(G)=D(G)+Tr(G), where D(G) denotes the distance matrix of graphs and Tr(G) is the diagonal matrix of vertex transmissions of G. For a given minimum dominating se...

A. GANAGI H. RAMANE H. WALIKAR

The Wiener index W(G) of a connected graph G is defined as the sum of the distances between all unordered pairs of vertices of G. The eccentricity of a vertex v in G is the distance to a vertex farthest from v. In this paper we obtain the Wiener index of a graph in terms of eccentricities. Further we extend these results to the self-centered graphs.

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