[Blueboard] Special Lecture on Graph Theory

evbagtas at mathsci.math.admu.edu.ph evbagtas at mathsci.math.admu.edu.ph
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


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

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


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.

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