Eigenvalues of graphs and a simple proof of a theorem of Greenberg

Pairing theorem of graph eigenvalues: It

Pairing theorem of graph eigenvalues: Its new proof and a generalization

✍ Mingzuo Shen 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 148 KB

## Abstract Each undirected graph has its own adjacency matrix, which is real and symmetric. The negative of the adjacency matrix, also real and symmetric, is a well‐defined mathematically elementary concept. By this negative adjacency matrix, the negative of a graph can be defined. Then an orthogo

A simple proof of Moser's theorem

✍ Zhu, Xuding 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB 👁 2 views

This article gives a simple proof of a result of Moser, which says that, for any rational number r between 2 and 3, there exists a planar graph G whose circular chromatic number is equal to r.

A simple proof of Menger's theorem

✍ William McCuaig 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 111 KB 👁 1 views

## Abstract A proof of Menger's theorem is presented.

A simple proof of Pancharatnam's theorem

✍ P.K. Aravind 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 465 KB

A Simple Proof of a Theorem of Milner

✍ Gyula O.H. Katona 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 174 KB

## Dedicated to the memory of Eric C. Milner A new short proof is given for the following theorem of Milner: An intersecting, inclusion-free family of subsets of an n-element set has at most ( n W(n+1)Â2X ) members.

A simple proof of a theorem of Jung

✍ Douglas Bauer; Aurora Morgana; E.F. Schmeichel 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 393 KB

Jung's theorem states that if G is a l-tough graph on n 3 11 vertices such that d(x) + d(y) 2 n -4 for all distinct nonadjacent vertices x, y, then G is hamiltonian. We give a simple proof of this theorem for graphs with 16 or more vertices.