# [Blueboard] Special Lecture on Graph Theory

Thu Jul 19 09:33:12 PHT 2012

```The Ateneo de Manila University
Mathematics Department

cordially invites you to a talk on

The Total Detection Number of Graphs
and other Graph Parameters

by

Henry E. Escuadro, PhD
Assistant Professor
Juniata College, PA

on Monday, July 23, 2012
4:30 - 5:30 pm at SECA 303.

Abstract

Let G be a connected graph and let c:E(G) -> {1, 2, ?, k} be a
labeling of the edges of G, not necessarily proper, that uses k
colors. For every vertex v of G, let code(v) = (a1, a2,?, ak) where ai
is the number of edges colored i that is incident with v. We say that
c is a detectable labeling of G if distinct vertices of G have
distinct codes. If c is a detectable k-labeling of G, the value of c
is given by val(c) = a1 + a2 + ? + ak. We define the total detection
number of G as the minimum among all val(c) where val(c) is taken over
all detectable labelings of G. In this talk, we give some results
regarding the total detection numbers of cycles, complete graphs, and
complete bipartite graphs. If time permits, I will also discuss some
interesting graph parameters that I had a chance to work on.

----------------------------------------------------------------
This message was sent using IMP, the Internet Messaging Program.

```