Graph Theory – Math Department, WCAS, Northwestern University
If the graph is directed and there is a unique edge e pointing from x to y, then we may write e = (x,y), so E may be regarded as a set of ordered pairs. is called pendant. The Handshaking Theorem. Let G = (V,E) be an undirected graph with e edges. Then 2e = X … Retrieve Content

Graph Terminology And Special Types Of Graphs Discrete …
Definition: Isolated and Pendant Vertices Definition A vertex of degree zero is called isolated. It follows that an graph that contains exactly one edge between each pair of distinct vertices. K 1 K 2 K 3 K 4 K 5 K 6 The graphs K n for 1 ≤ n ≤ 6 … Retrieve Document

Hamiltonicity In 3-connected Claw-Free Graphs
Kuipers and Veldman conjectured that any 3-connected claw-free graph with order ν and An edge e = uv is called a pendant edge if either d G(u) = 1 or d G(v) = 1. We use H ⊆ G to denote the fact that H is a subgraph of G. … Fetch Document

AUTOMORPHIC DECOMPOSITIONS OF GRAPHS
edge of G is a pendant edge if and only if it is incident with a pendant vertex. We say that of a graph H is a set of edge disjoint factors whose edge sets partition the edge set of H. In particular, an r-factorization is a factorization into r-factors [3]. … Fetch Doc

On Rainbow Coloring Of Some Classes Of Graphs
A path in an edge colored graph is said to be a rain bow path if no two edges on the path have the same color. from the helm graph by joining each pendant vertex to the central vertex of the helm. The flower graph has 2n+1 vertices, 4n-4 edges[14]. We … Doc Retrieval

Chapter 2 Graph Theory And Metric Dimension
The pendant vertex is called the pendant edge. A vertex of degree zero is called an isolated vertex. eis an edge of G, then G eis the graph obtained from Gby just deleting the edge ein G. 19. Graph Theory and Metric Dimension … Retrieve Full Source

GRAPH THEORY AND RELATED DATA STRUCTURES
Although in the definition of a graph neither the vertex set V nor the edge set E need be finite, Vertex v3 in Fig. 3-2 is a pendant vertex. Two adjacent edges are said to be in series if their common vertex is of degree two. … View Full Source

On The Spectral Radius Of Bicyclic graphs With Vertices And …
And adding a pendant edge to u(= v).Then ρ(G) Let uv be an edge of the connected graph G on n vertices. (i) If uv does not belong to an internal path of G, and G/= Cn, then ρ(Gu,v) > ρ(G). … Retrieve Content

Results On Total Restrained Domination In Graphs – HIKARI Ltd
pendant vertex to a graph G may arbitrarily increase or decrease the total restrained domination number. obtained from G by adding the pendant edge w4t, … Get Doc

Graph Terminology And The edge E The Vertices And
• If deg( v) = 1, v is called pendant. _____ The Handshaking Theorem: Let G = (V, E). Then 2|E the simple graph with – n vertices – exactly one edge between every pair of distinct vertices. Maximum redundancy in local area networks and … Content Retrieval

A Note On Singular Line graphs
K be the graph obtained by attaching a pendant edge to each vertex in C k:It can be seen that the line graph of G k has nullity one. Clearly G k has kspanning trees. Thus we have an in nite family of graphs, other than … Access Document

Number Of Loaded Vertices Of The Cycle In Unicyclic Reflexive …
Let G be a graph with a pendant edge , being of degree 1. Then. where ( ) is the graph obtained from G (resp. ) by deleting the vertex (resp. ) Theorem RS. Let G be a graph with a cut vertex u. If at least two components of G-u are . supergraphs. of Smith … Access This Document

Graph Theory – Analytic Technologies
Edges are also known as lines and (in social networks) as ties or links. An edge e = (u,v) is defined by while a vertex with degree 1 is a pendant. Holding average A bridge is defined as an edge whose removal would increase the number of components in the graph. Edge connectivity … Retrieve Full Source

A Family Of Well-Covered Graphs With Unimodal Independence …
K denotes the number of stable sets of cardinality k in graph G, and α(G) pendant edge to each vertex of G. Y. Alavi, P. J. Malde, A. J. Schwenk and P. Erd¨os (1987) asked whether for trees the independence polynomial is unimodal. V. E. … Content Retrieval

Graph Theory – Math Department, WCAS, Northwestern University
If the graph is directed and there is a unique edge e pointing from x to y, then we may write e = (x,y), so E may be regarded as a set of ordered pairs. is called pendant. A path is a sequence of vertices (vk) and edges (ek) of the form … Document Viewer

Delta-Wye Transformations And The Efficient Reduction Of Two …
1 are performed (other than loop or pendant edge reductions) it is necessary to define appropriate rela- 2-terminal graph to a single edge using the transfor- mations T1-T6, and to show the application of the DWR algorithm to two-terminal equilibrium prob- … Read Document

On Prime Labeling Of Some Classes Of Graphs
Graph labeling is an important area of research in Graph theory. There are many kinds of graph labeling such as Graceful labeling attaching a pendant edge at each vertex of the n-cycle. Definition 5: A Flower is the graph obtained from a Helmgraph by joining … Read Full Source

Total Colouring Regular Bipartite graphs Is NP-hard
For t > 3 let the graph S, be obtained from the complete bipartite graph K,- f,t by adding a pendant edge to each of the t vertices of degree t – 1. Then S, is a bipar- tite graph with 2t- 1 … Access Full Source

INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH …
Abstract: – A graph with vertex set V is said to have a prime labeling if its vertices are labeled with distinct integer 1,2,3 attaching a pendant edge at each vertex of the -cycle. In this paper we have proved that the graph obtained by … Doc Retrieval

A Characterization Of Graphs With Equal Domination Number And …
An edge incident with an end-vertex is called a pendant edge. A vertex adjacent to an dominating set of graph ′. Hence adding some pendant edges adjacent to vertices in … Retrieve Doc