Article Per Year (5 Year)
p-Index From 2021 - 2026
0.23
P-Index
This Author published in this journals
All Journal Journal of the Indonesian Mathematical Society
Paluga, Rolando N.
Unknown Affiliation
Mathematics

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
Monophonic Polynomial of the Join of Graphs Paluga, Rolando N.
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1686

Abstract

The monophonic polynomial of a graph $G$, denoted by $M(G,x)$, is the polynomial $M(G,x) = \sum_{k=m(G)}^{|G|}M(G, k)x^k $, where $|G|$ is the order of $G$ and $M(G, k)$ is the number of monophonic sets in $G$ with cardinality $k$. In this paper, we delve into some characterizations of monophonic sets in the join of two graphs and use it to determine its corresponding monophonic polynomial. Moreover, we also present the monophonic polynomials of the complete graph $K_n$ $(n \geq 1)$, the path $P_n$ $(n \geq 3)$, the cycle $C_n$ $(n \geq 4)$, the fan $F_n$ $(n \geq 3)$, the wheel $W_n$ $(n \geq 4)$, the complete bipartite $K_{m,n}$ $(m, n \geq 1)$, $P_m + P_n$ ($m, n \geq 3$), $C_m + C_n$ ($m, n \geq 4$), $P_m + C_n$ ($m \geq 3$ and $n \geq 4$), $P_m + \overline{K_n}$ ($m \geq 3$ and $n \geq 2$), and $C_m + \overline{K_n}$ ($m \geq 4$ and $n \geq 2$). In general, we obtain the monophonic polynomial of the join of two graphs.
Co-Authors