Average D-Distance Between Edges of a Graph
D. Reddy Babu,P. L. N. Varma +1 more
TLDR
In this paper, the average edge D-distance of a graph is defined as the average of the distance between all pairs of vertices of the graph, i.e., the distances between all edges in the graph.Abstract:
The D-distance between vertices of a graph G is obtained by considering the path lengths and as well as the degrees of vertices present on the path. The average D-distance of a connected graph is the average of the D-distance between all pairs of vertices of the graph. Similarly, the average edge D-distance is the average of D-distances between all pairs of edges in the graph. In this article we study the average edge D-distance of a graph. We find bounds for average edge D-distance which are sharp and also prove some other results.read more
Citations
More filters
Journal ArticleDOI
Radio analytic mean d-distance labeling of some basic graphs
TL;DR: In this paper, the radio analytic mean D-distance number of some basic graphs is computed, where d(u,v) denotes the distance between u and v, and diam(G) is the diameter of the graph.
Journal ArticleDOI
Radio mean D-distance number of cycle-related graphs
T. Nicholas,K. John Bosco +1 more
TL;DR: In this paper, the radio mean D-distance number of cycle-related graphs has been found for two distinct vertices u and v of a connected graph G, where d D (u, v) is the minimum value of rmn D (f) taken over all radio mean distance labels f of G and diam D (G) denotes the diameter of G.
Proceedings ArticleDOI
Mean vertex D-distance for radial and detour radial graphs
M. Suresh,V. Mohanaselvi +1 more
TL;DR: In this article, the Mean D-Distance, introduced by considering the degrees of various vertices presented in the path for some standard Radial and Detour Radial graphs, was introduced.
Journal Article
Radio Mean D-distance Number of Banana Tree, Thorn Star and Cone Graph
TL;DR: In this article, the radio mean D-distance number of a connected graph G is defined as an injective map f from the vertex set V(G) to N such that for two distinct vertices u and v of G, dD(u, v) + ⌈(f(u)+f(v))/2⌉ ≥ 1 + diamD(G).
References
More filters
Journal ArticleDOI
Mean distance in a graph
J. K. Doyle,Jack E. Graver +1 more
TL;DR: Borders for μ(Γ) are computed in terms of the number of vertices in Γ and the diameter of Γ to prove a formula for computing μ( Γ) whenΓ is a tree which is particularly useful when Γ has a high degree of symmetry.
Book ChapterDOI
Detour Distance in Graphs
TL;DR: In this paper, a graph G is called detour graph if d* (u, v) equals the standard distance between u and v in G for every pair u, v of vertices of G. Several results concerning detour distance and detour graphs are presented.
Journal Article
Detour distance in graphs
TL;DR: In this article, a graph G is called detour graph if d* (u, v) equals the standard distance between u and v in G for every pair u, v of vertices of G. Several results concerning detour distance and detour graphs are presented.
Journal ArticleDOI
Average distance and domination number
TL;DR: A sharp upper bound on the average distance of a graph of given order and domination number is given and the extremal graphs are determined.