TY  - JOUR
T1  - WIENER AND HARARY INDICES OF MYCIELSKIAN GRAPHS
AU  - Mittal, Tanya
AU  - Goyal, Shanu
PY  - 2025
DA  - November
Y2  - 2025
JF  - TWMS Journal of Applied and Engineering Mathematics
JO  - JAEM
PB  - Işık University Press
WT  - DergiPark
SN  - 2146-1147
SP  - 2687
EP  - 2696
VL  - 15
IS  - 11
LA  - en
AB  - Let $G = (V(G), E(G))$ be a graph, where $V= \{v_{1}, v_{2}, \ldots v_{n} \}$. Let $V' = \{ v'_{1}, v'_{2}, \ldots, v'_{n} \}$ be the twin of the vertex set $V(G)$. The Mycielskian graph $mathbb{M}(G)$ of $G$ is defined as the graph whose vertex set is $V(G) \cup V'(G) \cup \{w\}$ and the edge set is $E(G) \cup \{v_{i}v'_{j}: v_{i}v_{j}\in E(G) \} \cup \{v'_{i}w \in V'(G)  \}$. The vertex $v'_{i}$ is the twin of the vertex $v_{i}$ (or $v_{i} $ is twin of the vertex $v'_{i}$) and the vertex $w$ is the root of $\mathbb{M}(G)$. The closed Mycielskian graph $\mathbb{M}[G]$ of $G$ is defined as the graph whose vertex set is $V(G) \cup V'(G) \cup \{w\}$ and the edge set is $E(G) \cup \{v_{i}v'_{j}: v_{i}v_{j}\in E(G) \} \cup\{v_{i}v'_{i}: i = 1, 2, \ldots, n  \} \cup\{v'_{i}w \in V'(G)  \}$. The vertex $v'_{i}$ is the twin of the vertex $v_{i}$ (or $v_{i} $ is twin of the vertex $v'_{i}$) and the vertex $w$ is the root of $\mathbb{M}[G]$. In this paper, we study the Wiener and Harary indices of the Mycielskian and closed Mycielskian graphs.
KW  - closed splitting graph
KW  - shadow graph
KW  - closed shadow graph
KW  - Mycielskian
graph
KW  - closed Mycielskian graph
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UR  - https://dergipark.org.tr/en/pub/twmsjaem/issue//1814076
L1  - https://dergipark.org.tr/en/download/article-file/5376968
ER  -