# Papers

Journal of Ultra Scientist of Physical Sciences - A
Voulume: 29
Issue: 5
Article No. 1
Combinatorial Approach in Counting the Balanced Bicliques in the Join and Corona of Graphs
REGIMAR ADAN RASID (regimar.msu@gmail.com)
Department of Mathematics and Sciences, College of Arts and Sciences, Mindanao State University u2013 Tawi-Tawi College of Technology and Oceanography, Sanga-Sanga, 7500 Bongao, Tawi-Tawi, Philippines
ROSALIO GAID ARTES, Jr.
Department of Mathematics and Sciences, College of Arts and Sciences, Mindanao State University u2013 Tawi-Tawi College of Technology and Oceanography, Sanga-Sanga, 7500 Bongao, Tawi-Tawi, Philippines
Abstract :

In this paper, we characterized the balanced bicliques of graphs resulting from the join and the corona of graphs. Furthermore, we established the balanced biclique polynomials of the resulting graphs using combinatorial approach.

Keyword : Biclique, balanced biclique polynomials, join and corona of graphs, Mathematics Subject Classification (2000) MSC 05C15, 05C90
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Article No. 2
Path-Induced Geodetic Numbers of Some Graphs
RUTHLYN N. VILLARANTE (ruthlyn.villarante@g.msuiit.edu.ph)
Department of Mathematics and Statistics College of Science and Mathematics Mindanao State University-Iligan Institute of Technology Tibanga, 9200 Iligan City, Philippines
IMELDA S. ANIVERSARIO
Department of Mathematics and Statistics College of Science and Mathematics Mindanao State University-Iligan Institute of Technology Tibanga, 9200 Iligan City, Philippines
Abstract :

This study introduces a new geodetic invariant, the path-induced geodetic number of a connected simple graph G. We investigate its properties and characterize the path-induced geodetic sets of some common graphs. Also, the path-induced geodetic numbers of these graphs are determined

Keyword : geodesic, geodetic set, geodetic number, path-induced geodetic set, path-induced geodetic number, 2010 Mathematics Sub ject Classification: 05C12