**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