Distribution Number of the Kronecker and Vertex Gluing of Graphs

Distribution Number of the Kronecker
Product and Vertex Gluing of Graphs

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A RESEARCH PROPOSAL
Presented to
The Research Director of
Siquijor State College
Siquijor, Siquijor, Philippines

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Proponents
Dr. Ruben A. Sanchez 1
Dr. Baldomero R. Martinez 2
Dr. Michael P. Baldado Jr. 3
October 2012
1

Siquijor State College, Philippines
Siquijor State College, Philippines
3
Research Consultant, Negros Oriental State University, Philippines
2

TABLE OF CONTENTS

TITLE PAGE

i

TABLE OF CONTENTS

ii

LIST OF NOTATIONS

iii

LIST OF FIGURES

iv

1 INTRODUCTION
1.1 Objectives of the Study . . . . . . . . . .
1.2 Significance of the Study . . . . . . . . .
1.3 Scope and Limitations . . . . . . . . . .
1.4 Review of Related Literature and Studies
2 BASIC CONCEPTS
REFERENCES

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LIST OF NOTATIONS

Symbol
|S|
G
Kn
Km,n
G◦H
Cn σ(G) rad(G) diam(G) d(u, v)
E(G)
uv
Fn
Wn
G+H
NG (x)
V (G)
|V (G)|
Pn
S
K1
˙
X ∪Y
C3 = [1, 2, 3]

Name cardinality of set S complement of G complete graph of order n complete bipartite graph of order m + n corona of G and H cycle of length n
CDPU number of G radius of G diameter of G distance of vertices u and v edge set of G edge joining vertices u and v fan of order n + 1 wheel of order n + 1 join of G and H neighborhood of x in G vertex set of G order of G path of length n − 1 subgraph induced by S trivial graph G disjoint union cycle of order 3

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37
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11
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LIST OF FIGURES

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20

A graph G . . . . . . . . . . . . . . . . . . . . . .
A graph H which is an

References: Buczkowski, P.S., Chartrand, G., Poisson, C. & Zhang,P.(2003). (2005). On the metric dimension of some families of graphs, Electronic Notes in Discrete Math., 22 , 129-133.134 Chappell,G.G., Gimbel,J. & Hartman,C.(2010). Bounds on the metric Chartrand G., Eroh,L., Johnson,M.A., & Oellermann,O.R.(2000) Chartrand G., & Lesniak,L.(2000). Graphs and Digraphs, 3rd ed., Chapman and Hall/CRC,. Fehr M., Gosselin,S. & Oellermann,O.R.(2006). The metric dimension of Cayley digraphs, Discrete Math., 306, 31-41. Harary F. & Melter,R.A.(1976). On the metric dimension of a graph, Ars. Iswadi H., Baskoro,E.T., Simanjuntak,R., & Salman, A.N.M.(2012). The metric dimension of graph with pendant edges, URL:repository. Slater, P.J.(1975)., Leaves of trees, Congr. Numer., 14 , 549-559. 22 Slater, P.J.(1988)., Dominating and reference sets in graphs, J