International Journal of Fuzzy Mathematical Archive
  • Year: 2025
  • Volume: 24
  • Issue: 1

Cardinality of Hajós Graphs and Hajós Fuzzy Graphs on Fan Graph, Lollipop Graph, Friendship Graph, Tadpole Graph and Crown Graph

1PG and Department of Mathematics, Thanthai Periyar Government Arts and Science College (Autonomous), Affiliated to Bharathidasan University, Trichy -24

2PG and Department of Mathematics, Thanthai Periyar Government Arts and Science College (Autonomous), Affiliated to Bharathidasan University, Trichy -24, Corresponding author. Email: jasminekingslyalphonse@gmail.com

Online published on 7 February, 2026.

Abstract

Hajos Fuzzy graph is a new fuzzy graph obtained by applying a binary operation, named Hajos construction, on two fuzzy graphs. The Hajos construction on two (fuzzy) graphs produces many different (fuzzy) graphs depending on the choice of vertices and edges. The cardinality of Hajos (fuzzy) graphs is the total number of Hajos (fuzzy) graphs from two given Hajos (fuzzy) graphs. Here, the cardinality of Hajós fuzzy graphs are determined for any two fuzzy graphs based on the permutations and combinations method.is By this concept, the cardinality of Hajós (fuzzy) graphs is derived for the combinations of the two (fuzzy) graphs, such as the fan graph, lollipop graph, friendship graph, tadpole graph and crown graphs.

Keywords

Hajos Fuzzy Graph, Cardinality, Fan Graph, Lollipop Graph, Friendship Graph, Tadpole graph and Crown Graph, 94D05